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Brent$117.6Gas TTF$1,192USD453.87 ₸
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EconomicsUncertainty, risk and decisions Intermediate 29 min read

Market, financial and regulatory uncertainty

Market, financial and regulatory uncertainty is the inexact knowledge of what comes into a project from outside. It covers the prices of oil and gas, the cost of services and equipment, exchange rates and inflation, interest rates and access to money, the taxes and rules that the state will set, and the behaviour of partners. Unlike the uncertainty of the subsurface, no well can reduce it. We can describe it, pass part of it to others, and allow for it in the decision.

Why it matters

The oil price and taxes are the strongest levers of the value of any oil project, and they are exactly what an engineer knows least about. The mistake here is not a wrong forecast, because a price forecast is almost always wrong. The mistake is to take decisions as if the future price were known. The lesson shows how to describe external uncertainty in numbers and how it changes the distribution of NPV. It explains why costs, the exchange rate and taxes are linked with the price, and how to value the flexibility of a project.

Quick refresher

  • External uncertainty cannot be reduced by studies. It can only be described, partly passed to others (hedging, contracts, stabilisation clauses, the structure of financing), and allowed for in the decision. A stabilisation clause is a term that protects the investor from harmful changes of the rules after the money is spent.
  • In the short term, the demand for oil and its supply react weakly to the price, so a small supply disruption raises the price by tens of per cent. We measure the changeability, called the volatility, as the standard deviation of the logarithmic returns. We turn it into a yearly figure by multiplying by the square root of the number of periods in a year.
  • A forward curve is the set of delivery prices for future dates, at which a deal can be made today. Contango (future prices above the spot price, which is the price for immediate delivery) is limited by the cost of storage and of money. Backwardation (future prices below the spot price) is not limited by anything: in a shortage, the spot price can be much higher than future prices.
  • A price model is also an assumption. With the same yearly volatility of 25%, the probability of a negative NPV of the example project is 23% with a random-walk price and 2% with mean reversion.
  • External variables are linked: contractors charge more when oil is expensive, the tenge strengthens when oil is expensive, and the state raises taxes when prices are high. Some links reduce the risk, and others cut off the gain. We set them in scenarios and in simulation explicitly.
  • Debt raises both the return and the risk for shareholders, and the lender looks at the coverage of the debt in each year. Flexibility, which is the possibility to wait, to expand or to stop a project, is worth money, and the more so the higher the uncertainty.
Key relationships
σyr=σΔt 1/Δt\sigma_{\text{yr}} = \sigma_{\Delta t}\,\sqrt{1/\Delta t}

yearly volatility from the returns over a period Δt\Delta t (years): for months, ×12\times\sqrt{12}

FT≤S0 (1+r)T+UTF_T \le S_0\,(1+r)^{T} + U_T

the upper limit of the forward price: spot plus interest and storage

vt=σ2 1−φ2t1−φ2v_t = \sigma^2\,\frac{1 - \varphi^{2t}}{1 - \varphi^{2}}

variance of the logarithm of the price after tt years with mean reversion; at φ=1\varphi = 1 it is σ2t\sigma^2 t

ROE=ROA+DE (ROA−rd)\mathrm{ROE} = \mathrm{ROA} + \frac{D}{E}\,(\mathrm{ROA} - r_d)

the return on equity at a ratio of debt to equity D/ED/E

DSCRt=CFADStIt+At\mathrm{DSCR}_t = \frac{\mathrm{CFADS}_t}{I_t + A_t}

debt coverage: the cash flow available for debt service divided by the interest and repayment of the year

Common pitfalls
  • Taking one price scenario for a forecast and building the decision as if the price were known.
  • Setting costs, the exchange rate and taxes independently of the price: in the “worst” scenario impossible combinations appear, and the real links are lost.
  • Taking the forward price for a forecast of the future price, and mixing nominal futures with a model in constant prices.
  • Putting the whole regulatory risk into a premium on the rate: it “punishes” distant flows with no link to concrete events.
  • Judging a project with debt by the IRR of the project: shareholders care about the cash flow after debt service and the margin against the covenants.

After this lesson you can

  • name the sources of external uncertainty of a project and explain how they differ from technical uncertainty
  • explain why the oil price is so changeable, calculate volatility from a series of prices, and read a forward curve, contango and backwardation
  • compare the price models, the random walk and mean reversion, and build a simulation of the NPV of a project from them
  • estimate how costs that follow the price, the tenge exchange rate and changes in taxes act on a project, taking their link with the price into account
  • calculate how debt raises the risk for shareholders (the IRR of equity, which is the return on the shareholders' own money, and the debt service coverage ratio), and estimate the value of flexibility with a simple real option (the right, but not the duty, to act later)

Uncertainty that a well cannot reduce

We reduce the uncertainty of the subsurface (volumes, flow rates, recovery) with data: appraisal wells, studies, experience of development (Geological and technical uncertainty of a project). External uncertainty is different by nature. No study will make the oil price in five years more exact, and a government's decision on a tax does not depend on the quality of the reservoir model. We can only describe it, by a range, a distribution or scenarios. We can pass part of it to others for a fee, and we can allow for it in the decision.

Sources of external uncertainty of a project
Source
Product market
What is known inexactly
the prices of oil, gas and oil products; the price differences between grades and delivery points
How it is managed
hedging, gas contracts, flexibility of the project
Source
Costs
What is known inexactly
the prices of services, equipment, materials and labour
How it is managed
fixed-price contracts, the timing of purchases
Source
Currency and inflation
What is known inexactly
the exchange rate of the tenge to the dollar, the growth of prices
How it is managed
matching the currencies of revenue, costs and debt; indexation
Source
Financing
What is known inexactly
interest rates, access to credit, the terms of lenders
How it is managed
the structure of the debt, a fixed rate, a margin against the covenants (the conditions set by the lender)
Source
The state
What is known inexactly
taxes, duties, regulation, the terms of the contract
How it is managed
stabilisation clauses, arbitration, diversification across countries
Source
Partners
What is known inexactly
the decisions, money and interests of the other participants
How it is managed
a joint operating agreement, the right to vote

Hedging, insurance, contracts and project finance are covered in the lesson on the transfer of risk.

External risks have three common features. They are common to all the projects of a company: a fall of the oil price hits all the fields at once, so diversification across areas does not protect against it (diversification of a company). They are linked with each other: contractors charge more when oil is expensive, the tenge strengthens when oil is expensive, and taxes grow together with the price. They do not disappear with time: technical uncertainty turns into knowledge by the end of development, while the price and the taxes stay unknown until the last year.

Oil and gas prices: where the swings come from

Oil is a world commodity: its price is made by the demand and supply of the whole world, and its changes reach almost any field at once. The demand for oil is derived: what we need is not oil itself but petrol, diesel, aviation fuel and raw material for chemicals. In a crisis, when fewer goods are carried and fewer people fly, demand falls within a few months. Efficient engines, electric cars and gas instead of oil change it slowly, over years. Supply depends on the decisions of the producing countries. These include the agreements of OPEC+ (the Organization of the Petroleum Exporting Countries and the countries that joined its decisions, among them Kazakhstan). Supply also depends on investments of past years, accidents, wars and sanctions.

The main reason why the price swings so much is that demand and supply react weakly in the short term. In other words, the price elasticity is low (consumption changes little when the price changes). The cars, aircraft and factories are already bought, and the wells are already drilled. To change equipment and habits, or to bring in new fields, takes years. So, while consumers and producers have not had time to adapt, even a small shortage or surplus of oil moves the price by tens of per cent. With time the reaction grows, and the price comes back. The mechanism and the calculation of the jump in price when supply is disrupted are covered in the lesson on the history of the oil industry. For the assessment of a project, the consequence matters: a high price itself creates forces that lower it, and a low price does too. The model of mean reversion of the price (the section below) is based on this.

Grades and delivery points. Oil is sold at the prices of benchmark grades (the standard oils that other prices are quoted against), such as Brent, WTI (West Texas Intermediate) and Dubai, with a premium or a discount. The difference, the differential, depends on quality (light low-sulfur oil is dearer, because it gives more light products), on the distance to the buyer and on what the market lacks now. It also changes. According to the National Bank's estimate, in September 2026 the Kazakhstan blend CPC Blend was sold at a premium of US$2–4 to Dated Brent (the price of physical North Sea oil for loading in the next few weeks), although it usually sells at a discount (MunaiHub weekly review, September 2026). The price at the field, the netback, is found by subtracting transport and the discount (price and revenue).

Gas. There is no single world price of gas: in Europe, Asia and North America it can differ several times over. The reason is transport. Gas goes by pipeline, or it is liquefied and carried by tankers, and per unit of energy this costs much more than carrying oil. In ordinary conditions, gas with the same energy takes about a thousand times more volume. The price risk of a gas project is largely set by the contract. If the gas price is tied to oil or to oil products, the project gets the volatility of oil. If it is tied to the exchange price of gas, it gets the volatility of its regional market. A take-or-pay condition, under which the buyer pays for an agreed share of the volume even if it did not take it, protects the seller from a fall of demand. A long contract with a fixed formula reduces the price risk, but leaves the risk that the formula will turn out unfavourable.

In Kazakhstan the price of gas for many producers is not set by the market. The state, through the national operator, the national gas company QazaqGaz, has a pre-emptive right: it can buy first the raw and commercial gas that subsoil users sell. The price covers the costs of production, processing and transport plus a profit margin of no more than 10%. For the gas of new areas under contracts after 1 January 2023, the price is set by a formula tied to the export price and to the domestic price caps. There are exceptions, for example the gas of gas and gas-condensate fields (the Law “On Gas and Gas Supply”, Article 15). The Ministry of Energy sets the wholesale price caps of commercial gas on the domestic market (the same law, Articles 6 and 20). The rules of the Ministry of Energy are on the pages of the “Legislation” section of MunaiHub. A regulated price reduces the price risk but replaces it with a regulatory one: the state can change the formula.

Volatility and the forward curve

We measure the changeability of the price by the volatility: the standard deviation (the usual measure of spread) of the logarithmic returns ln⁡(Pt/Pt−1)\ln(P_t/P_{t-1}) over a chosen period. A logarithmic return is the logarithm of the ratio of two successive prices; for small changes it is simply the percentage change. We take logarithms because the price changes in per cent, not in dollars: a rise from 50 to 60 and a rise from 100 to 120 US$/bbl are the same relative change. Volatilities over different periods are brought to a year.

Yearly volatility
σyr=σΔt 1Δt,σΔt=sd[ln⁡PtPt−1]\sigma_{\text{yr}} = \sigma_{\Delta t}\,\sqrt{\frac{1}{\Delta t}}, \qquad \sigma_{\Delta t} = \mathrm{sd}\left[\ln\frac{P_t}{P_{t-1}}\right]
where:
  • σyr\sigma_{\text{yr}}yearly volatility, fraction per year
  • σΔt\sigma_{\Delta t}sample standard deviation of the returns over the period Δt\Delta t, fraction per period
  • Δt\Delta tlength of the period: a month is 1/121/12 of a year, a trading day is about 1/2521/252, years
  • PtP_tprice at the end of the period tt, US$/bbl

Units: fractions (in the text, per cent)

Holds when
  • the returns of adjacent periods are independent; then their variances add up, and the standard deviation grows as the square root of time
  • if the price has mean reversion, over long periods the spread grows more slowly than the root (see the section on price models)

A volatility of 30% a year means that over a year the price will change, with a probability of about two thirds, by no more than about 30% in one direction or the other, provided that the price has a log-normal distribution.

Worked exampleVolatility from monthly prices
Given (assumed data)
Prices at the end of the month, 13 months
68.0, 71.5, 69.0, 74.5, 79.0, 76.5, 70.0, 65.5, 67.0, 62.5, 66.0, 70.5, 73.0 US$/bbl (assumed)
Solution
  1. Returns for a month: ln⁡(71.5/68.0)=0.0502\ln(71.5/68.0) = 0.0502, ln⁡(69.0/71.5)=−0.0356\ln(69.0/71.5) = -0.0356 and so on, 12 values in all.
  2. Their mean is 0.0059, and the sample standard deviation is σmo=0.0602\sigma_{\text{mo}} = 0.0602.
  3. The yearly volatility: 0.0602⋅12=0.0602⋅3.464=0.2090.0602\cdot\sqrt{12} = 0.0602\cdot3.464 = 0.209, about 20.9%.
  4. In a year the price will, with a probability of about 68%, be between 73.0 e−0.022−0.209=57.973.0\,e^{-0.022 - 0.209} = 57.9 and 73.0 e−0.022+0.209=88.073.0\,e^{-0.022 + 0.209} = 88.0 US$/bbl. The correction σ2/2=0.022\sigma^2/2 = 0.022 keeps the expected price equal to the present one.
Answer: The yearly volatility of the series is about 20.9%. In a year the price will be, in two cases out of three, within 57.9–88.0 US$/bbl.

What it means. Twelve observations give a rough estimate: another year of the same market can easily give 15 or 35%. That is why we calculate volatility from long series, from daily prices over years, and check that it has not changed. Monthly prices must be taken at the end of the month: monthly averages smooth the swings and understate volatility. The data in this example are assumed for illustration.

Brent: the average price, the range and the yearly volatility, from daily spot prices
Year
2008
Average, US$/bbl
96.94
Lowest and highest
33.73–143.95
Volatility
50%
Year
2014
Average, US$/bbl
99.02
Lowest and highest
55.27–115.19
Volatility
18%
Year
2015
Average, US$/bbl
52.32
Lowest and highest
35.26–66.33
Volatility
41%
Year
2020
Average, US$/bbl
41.96
Lowest and highest
9.12–70.25
Volatility
115%
Year
2022
Average, US$/bbl
100.93
Lowest and highest
76.02–133.18
Volatility
47%
Year
2024
Average, US$/bbl
80.52
Lowest and highest
70.31–93.12
Volatility
27%
Year
2025
Average, US$/bbl
69.14
Lowest and highest
59.93–83.48
Volatility
31%
Year
2026, to 14 October
Average, US$/bbl
94.85
Lowest and highest
61.08–138.21
Volatility
70%

MunaiHub calculation from the daily Brent spot prices of the US Energy Information Administration (EIA), read on 17 October 2026. The average is over working days, and the volatility is the standard deviation of the daily logarithmic returns multiplied by 252\sqrt{252}. The data refer to the years named and do not describe the current market.

In calm years the volatility of Brent is about 20–30% a year, and in crises it is two to four times more. The figures of the table show something else too: in one year the price can fall several-fold (2008, 2020), or more than double (2026). A project designed for a “flat” price will go through several such years during its life.

The forward curve. Besides the price “today”, the spot price, the market gives delivery prices for future dates. They come from futures (standard contracts traded on an exchange) and from forward contracts (private agreements to deliver later at a price fixed now). The set of these prices by delivery date is called the forward curve. If the future prices are higher than the spot price, the curve is called contango, and if they are lower, backwardation.

Prices of WTI futures for delivery in 1–4 months, US$/bbl
Date
17 April 2020 (contango)
1st month
18.27
2nd
25.03
3rd
29.42
4th
31.20
Date
8 March 2022 (backwardation)
1st month
123.70
2nd
119.65
3rd
115.21
4th
110.83

Settlement prices of contracts 1–4 of the New York Mercantile Exchange, from EIA data. On 20 April 2020 the nearest (May) contract closed at minus US$37.63/bbl: during the pandemic demand fell, and the storage at the delivery point was filling up, so the holders of contracts paid money not to have to take the oil. The data refer to the dates named.

The upper limit of the forward price (the cost of carry)
FT≤S0 (1+r)T+UTF_T \le S_0\,(1 + r)^{T} + U_T
where:
  • FTF_Tforward price for delivery in TT years, US$/bbl
  • S0S_0spot price today, US$/bbl
  • rrinterest rate per year: the cost of the money put into the oil, fraction per year
  • UTU_Tcost of storing a barrel until the delivery date, US$/bbl
  • TTtime to delivery, years

Units: any currency, nominal money

Holds when
  • there is free storage and money at the rate rr; otherwise the limit shifts
  • there is no lower limit: storage does not help someone who needs the oil now

If the forward price is above the spot price plus the cost of carry (the cost of storage and of the money tied up in the oil), it pays to buy oil, store it and sell it by the forward, with no price risk. Such deals raise the spot price and lower the forward price until the gain disappears. So contango is never larger than the cost of storage and of money.

Worked exampleStoring oil for the forward
Given (assumed data)
Spot
$80/bbl
Rate
5% a year
Storage
$0.6/bbl a month, for 6 months
Six-month forward
$88/bbl
Solution
  1. Oil bought today and sold in 6 months costs 80⋅1.050.5+0.6⋅6=81.98+3.6=85.5880\cdot1.05^{0.5} + 0.6\cdot6 = 81.98 + 3.6 = 85.58 US$/bbl.
  2. The forward price of 88 is higher: to buy, store and sell by the forward brings 88−85.58=2.4288 - 85.58 = 2.42 US$/bbl with no price risk.
  3. Such deals go on until the spot price rises or the forward price falls enough that the gain disappears.
Answer: The limit of the six-month forward price is $85.58/bbl. At $88/bbl, storage brings 2.42 dollars a barrel with no risk.

What it means. The upper limit of contango is set by storage and by the cost of money. When the storage is almost full, storage becomes dearer, and contango becomes steeper, as in the spring of 2020. The curve has no lower limit: in a shortage, the holders of oil will not sell it cheaply for a future delivery. The data in this example are assumed for illustration.

Backwardation can be very steep. According to EIA data, on 9 October 2026 the spot price of Brent was US$130.03/bbl, and the December Brent futures on the ICE exchange (Intercontinental Exchange) cost about US$104 that evening (MunaiHub weekly review). The market was paying a quarter more for oil now than for oil in two months.

Price models and simulation of NPV

To go from one price scenario to a distribution of NPV, we need a model of how the price can change from year to year. There are two simple models. In the random walk, each year the price gets a random push, and the push stays forever: the uncertainty grows without limit. In mean reversion, the deviation of the price from its long-term level partly disappears each year, because a high price causes more production and savings, and a low price causes less investment.

Price as a random process: the walk and mean reversion
Xt=φ Xt−1+σ εt,Pt=Pˉ exp⁡(Xt−12vt),vt=σ2 1−φ2t1−φ2X_t = \varphi\,X_{t-1} + \sigma\,\varepsilon_t, \qquad P_t = \bar P\,\exp\left(X_t - \tfrac{1}{2}v_t\right), \qquad v_t = \sigma^2\,\frac{1 - \varphi^{2t}}{1 - \varphi^{2}}
where:
  • XtX_tdeviation of the logarithm of the price from the level ln⁡Pˉ\ln\bar P in year tt; X0=0X_0 = 0, —
  • φ\varphithe share of the deviation that remains after a year: 1 is a random walk, less than 1 is mean reversion, —
  • σ\sigmayearly volatility, the standard deviation of the yearly push, fraction per year
  • εt\varepsilon_tindependent standard normal random numbers, —
  • Pˉ\bar Pthe expected price of each year, US$/bbl
  • vtv_tvariance of XtX_t; at φ=1\varphi = 1 it equals σ2t\sigma^2 t, —

Units: prices in constant dollars of the base year

Holds when
  • the correction −vt/2-v_t/2 keeps the expected price of each year equal to Pˉ\bar P: the models change the spread, not the average level
  • the logarithm of the price is normally distributed, and the price is log-normal and in the model cannot become negative
  • φ\varphi and σ\sigma are constant; in reality volatility changes, and the long-term level of the price is unknown and changes too

With mean reversion, the variance does not grow without end but tends to a limit σ2/(1−φ2)\sigma^2/(1 - \varphi^2). A deviation fades by half in 1.361.36 years at φ=0.6\varphi = 0.6 (the derivations are in the advanced section).

80% price bands with a random walk and with mean reversion, with the same yearly volatility0246810020406080100120Years from todayPrice, US$/bblrandom walkmean reversionexpected price

Chart: the horizontal axis shows years from 0 to 10, and the vertical axis shows the price from 0 to 120 dollars per barrel. Both bands start at the point 50. The band of the random walk widens without limit: after 8 years from 16 to 96, after 10 years from 13 to 101. The band of mean reversion reaches, within 2–3 years, a width from 32 to 71 and does not widen further. The horizontal dotted line is the expected price, 50.

CalculatedThe bands into which the price falls with a probability of 80% (from the 10th to the 90th percentile), with a random walk and with mean reversion. The yearly volatility of both models is 25%, and the expected price of each year is $50/bbl. After 8 years the band of the walk is about twice as wide.
Worked exampleThe NPV of a project at a random price: two models
Given (assumed data)
Project
from the library's examples (Net present value (NPV)); NPV at 10% and a constant price of $50/bbl is 100.1 million dollars
Price in years 2–9
random; the expected price of each year is $50/bbl; the yearly volatility is 25% (assumed)
Models
random walk (φ=1\varphi = 1) and mean reversion (φ=0.6\varphi = 0.6; a deviation fades by half in 1.36 years)
Trials
10,000; the same random numbers for both models
Solution
  1. The first trial: ε1=−1.0590\varepsilon_1 = -1.0590, ε2=0.0449\varepsilon_2 = 0.0449, ε3=−2.2909\varepsilon_3 = -2.2909 … For year 2 both models give X1=0.25⋅(−1.0590)=−0.26475X_1 = 0.25\cdot(-1.0590) = -0.26475 and a price of 50 e−0.26475−0.03125=37.1950\,e^{-0.26475 - 0.03125} = 37.19 US$/bbl.
  2. Year 3. Walk: X2=−0.26475+0.25⋅0.0449=−0.253525X_2 = -0.26475 + 0.25\cdot0.0449 = -0.253525, v2=0.125v_2 = 0.125, price 50 e−0.253525−0.0625=36.4550\,e^{-0.253525 - 0.0625} = 36.45. Reversion: X2=0.6⋅(−0.26475)+0.25⋅0.0449=−0.15885+0.011225=−0.147625X_2 = 0.6\cdot(-0.26475) + 0.25\cdot0.0449 = -0.15885 + 0.011225 = -0.147625, v2=0.36⋅0.0625+0.0625=0.085v_2 = 0.36\cdot0.0625 + 0.0625 = 0.085, price 50 e−0.147625−0.0425=41.3450\,e^{-0.147625 - 0.0425} = 41.34 US$/bbl.
  3. The prices of years 3–9 in this trial: with the walk 36.5, 19.9, 14.2, 17.8, 17.7, 17.2, 19.5; with reversion 41.3, 24.6, 23.5, 40.3, 44.2, 45.6, 54.4 US$/bbl. The project model gives an NPV of −73.6 and 14.6 million dollars.
  4. Over all the trials, the walk: the mean NPV is 99.3, the standard deviation is 137.4 million dollars; P90 is −41, P50 is 72, P10 is 273 million dollars; NPV is negative in 22.7% of the trials.
  5. Mean reversion: the mean is 99.9, the standard deviation is 60.4; P90 is 28, P50 is 94, P10 is 180 million dollars; NPV is negative in 2.3% of the trials.
  6. A check: the average price of year 9 over the trials is 49.7 and 49.8 US$/bbl. The models change the spread of the price, not its average level.
Answer: The mean NPV in both models is close to 100.1 million dollars, but the probability of a loss is 22.7% with a random walk and 2.3% with mean reversion.

What it means. The mean NPV is almost equal to the NPV at a constant price: the income of the project is almost proportional to the price, and the expected price is the same. The difference is smaller than the random error of the simulation itself: the standard error of the mean (the typical error of a mean found from a sample) with 10,000 trials is 1.4 and 0.6 million dollars. The one non-linearity of the model is the income tax: it does not refund the loss of a low year but only carries it forward to later years (non-linearity). So with a random walk, when the price can stay low for years, the expected NPV is slightly below the NPV at a constant price. With mean reversion such years are rare, and the difference is hardly visible. The main difference is in the spread. With the walk, the bad years add up, and the price can stay low for years. With mean reversion the deviations fade. The statistics of prices do not tell clearly which model is closer to the truth. Distant futures swing less than near ones, which points to a partial reversion. So the choice of a price model is an assumption of the same kind as the volatility, and we show it together with the result. How simulation works in general is covered in the lesson on scenarios. The data in this example are assumed for illustration.

Probability that the NPV of the project is not less than a given value, with a random walk and with mean reversion of the price−10001002003004000%20%40%60%80%100%NPV at 10%, US$ millionProbability of exceedancerandom walkmean reversion

Two falling curves: the horizontal axis shows NPV from minus 100 to 400 million dollars, and the vertical axis shows probability from 0 to 100 per cent. The mean-reversion curve is steep: it passes through 98 per cent at zero NPV, through 90 per cent at 28, through 50 per cent at 94 and through 10 per cent at 180 million. The random-walk curve is gentle: 77 per cent at zero NPV, 90 per cent at minus 41, 50 per cent at 72 and 10 per cent at 273 million.

CalculatedThe probability that the NPV of the example project will be not less than a given value, with a random price (10,000 trials): a random walk and mean reversion with the same yearly volatility of 25%. The vertical line is zero NPV.

Costs, the tenge exchange rate and inflation

Costs follow the price. When oil gets dearer, companies drill and build more, drilling rigs, vessels and crews are busy, and contractors raise their rates. After a year or two new equipment comes to the market, and the rates fall. When oil gets cheaper, services get cheaper after it, with a delay. This link partly reduces the price risk, and we need to set it explicitly in scenarios (consistent scenarios).

Worked exampleCosts that follow the price
Given (assumed data)
Project
from the library's examples, NPV at 10%
Link
capital and operating expenditure change by 0.4% when the price changes by 1% (assumed)
Prices
$35/bbl and $65/bbl, 30% below and above the base
Solution
  1. At $35/bbl with the costs unchanged, NPV = 14.83 million dollars. If the costs have become cheaper by 0.4⋅30=120.4\cdot30 = 12%, NPV = 36.32 million dollars.
  2. At $65/bbl: 185.44 million dollars with the costs unchanged, and 163.94 if the costs have risen by 12%.
  3. The swing of NPV between the two prices: 185.44−14.83=170.61185.44 - 14.83 = 170.61 without the link, and 163.94−36.32=127.62163.94 - 36.32 = 127.62 million dollars with the link.
  4. The break-even price by NPV: $32.4/bbl with the costs unchanged, and $26.5/bbl with the costs that follow the price.
Answer: The link of costs with the price narrows the swing of NPV by 25% and lowers the break-even price from $32.4/bbl to $26.5/bbl.

What it means. The link works in both directions: when oil is expensive, contractors take part of the gain. It is incomplete and delayed: the costs under contracts already signed and equipment already bought do not depend on the price. So in the first years after a fall of the price, the project is protected less than the calculation shows. The size of the link is assumed; we estimate it from the history of the prices of services in the region. The data in this example are assumed for illustration.

The tenge exchange rate. Oil is sold for dollars, but a large part of the costs (wages, local services, electricity) and the taxes are paid in tenge. A weaker tenge reduces these costs in dollars and improves the dollar flow of an exporter. A stronger tenge makes it worse. With time, local prices rise after the weakening of the currency, and part of the gain disappears (inflation and currency). For a company that sells on the domestic market for tenge but owes in dollars, the picture is the opposite: a weaker tenge increases its debt in tenge (currency risk).

Sharp changes of the tenge rate, and the price of Brent on those days
Dates
4 February 2009 → 6 February 2009
Official rate, ₸ per US dollar
122.32 → 149.97
The dollar rose
by 22.6%
Brent, US$/bbl
43.68
Dates
11 February 2014 → 13 February 2014
Official rate, ₸ per US dollar
155.56 → 184.50
The dollar rose
by 18.6%
Brent, US$/bbl
109.21
Dates
20 August 2015 → 21 August 2015
Official rate, ₸ per US dollar
188.38 → 255.26
The dollar rose
by 35.5%
Brent, US$/bbl
45.63

The official rates of the National Bank of Kazakhstan on the dates stated; the price of Brent is the spot price, from EIA data, on the first date. On 20 August 2015 the government and the National Bank announced a move to a freely floating exchange rate and to inflation targeting.

The devaluations (sharp falls of the tenge) of 2009 and 2015 came after a collapse of the oil price. On 3 July 2008 Brent cost US$143.95/bbl, in August 2014 it averaged about 100, and on the days of the devaluations it was 44–46. February 2014 shows that the rate does not depend on oil alone: Brent then cost $109/bbl. The link with oil works in the other direction too: in 2026, when oil got dearer, the tenge strengthened, from 505.53 tenge per dollar on 2 January to 452.12 on 17 October, by 12% (the official rates of the National Bank). The republican budget for 2026 was calculated at a price of $60/bbl and a rate of 540 tenge per dollar, and the draft budget for 2027 at $70/bbl and 480 tenge (the forecast for the budget of 2026–2028; MunaiHub weekly review, September 2026).

Worked exampleA strong tenge and the dollar costs of an exporter
Given (assumed data)
Operating costs
$15/bbl at a rate of 505.53 ₸ per US dollar (2 January 2026); 60% of them are paid in tenge (assumed)
Rates
452.12 ₸ per US dollar (17 October 2026) and, for comparison, 600 ₸ per US dollar (assumed)
Assumption
the tenge costs have not changed in tenge
Solution
  1. The tenge part: 0.6⋅15=90.6\cdot15 = 9 dollars, or 9⋅505.53=4549.779\cdot505.53 = 4549.77 ₸ a barrel.
  2. At 452.12 ₸ per dollar: 4549.77/452.12=10.064549.77/452.12 = 10.06 dollars; the costs are 6+10.06=16.066 + 10.06 = 16.06 US$/bbl, which is 7.1% more.
  3. At 600 ₸ per dollar: 4549.77/600=7.584549.77/600 = 7.58 dollars; the costs are 6+7.58=13.586 + 7.58 = 13.58 US$/bbl, which is 9.5% less.
Answer: A strengthening of the tenge by 12% raised the dollar costs of the exporter from $15/bbl to $16.06/bbl. A weakening to 600 ₸ would have lowered them to $13.58/bbl.

What it means. In the same months the average spot price of Brent rose from $66.6/bbl in January 2026 to $127.0/bbl in the first half of October (EIA). The revenue per barrel almost doubled, while the costs rose by 7.1%. For an exporter the link “expensive oil, strong tenge” is a partial natural protection. In good times it takes away a little of the gain, and in bad times, when oil gets cheaper and the tenge weaker, it softens the blow. The tenge prices themselves change over a year, so in a model the exchange rate and inflation are set together. The share of the tenge costs is assumed.

Inflation. Expected inflation by itself hardly affects the real NPV, if the flow and the rate are consistent. The risk comes from unexpected inflation and from its unevenness. The tax deductions for depreciation are not indexed, long contracts with a fixed price lose their real value, and the oil price does not have to rise together with local prices (where inflation is not neutral).

Taxes and rules: the risk of changing conditions

The investor knows, before the investment decision, the taxes and duties, the requirements for safety, environmental protection and gas flaring, and the rules for purchases from local suppliers and for deliveries to the domestic market. It puts them into the cash flow like any other costs. What creates uncertainty is something else: the conditions may change when the money is already invested and one cannot leave the project without loss.

Why do conditions change? Before investing, the investor can choose another country. After that, the platform and the pipeline cannot be taken away, and the bargaining power passes to the state. Conditions that suited both sides at a price of $50/bbl seem to the state too soft at $100. This is called the “obsolescing bargain”: the deal goes out of date. So taxes are most often raised when oil is expensive. A windfall tax is introduced (it takes a share of the extra income that high prices bring), and rates and duties are raised. Tax breaks are given when oil is cheap and there is not enough investment. A budget deficit can raise taxes with no link to the price.

  • Taxes and duties: rates, bases, scales, deductions; new windfall taxes.
  • The product market: export duties and bans, compulsory deliveries to the domestic market, regulation of the prices of gas and oil products.
  • Technical requirements: new standards of safety or environmental protection, applied retroactively to facilities that already operate; a ban or a limit on gas flaring (associated gas).
  • Contract and law: revision of the terms, limits on selling interests, and in the extreme case the termination of the contract or nationalisation.

A stabilisation clause is a condition of a contract or a law that protects the investor from changes that make its position worse. Freezing clauses apply the law as of the date of the contract to the project. Economic equilibrium clauses let the changes apply, but the state must restore the investor's economic position, by compensation or by changing other terms. A clause does not make the risk zero. It usually does not extend to safety and to the protection of nature and health, and its enforcement may need a long international arbitration (a case heard by independent arbitrators).

In Kazakhstan the Subsoil Code protects signed contracts from changes of legislation that worsen the results of the subsoil user. This does not apply to national security, defence, environmental safety, health care, taxation, customs regulation and the protection of competition (Article 36). So the tax terms of most contracts change together with the Tax Code. A stable tax regime is kept by production sharing agreements concluded before 1 January 2009 that passed the compulsory tax examination, and by contracts approved by the President, for the taxes whose stability is directly stated in them (Article 755 of the Tax Code; in more detail). An example of a change already adopted: from 2027 the rate of the mineral extraction tax (MET) on oil will be taken from a matrix “annual production × world price”, and the oil of the payers of this tax is released from the rent tax on export (how the regime is changing).

Worked exampleA possible rise of royalty: a probability, or a premium on the rate
Given (assumed data)
Project
from the library's examples; royalty 10%, income tax 20%
Event
with a probability of 0.3, from year 5 the royalty becomes 15% (assumed)
Rate
10%
Solution
  1. If the rise happens, the NPV of the project is 90.59 million dollars instead of 100.13. The loss is 100.13−90.59=9.54100.13 - 90.59 = 9.54 million dollars.
  2. Expected NPV: 0.7⋅100.13+0.3⋅90.59=97.270.7\cdot100.13 + 0.3\cdot90.59 = 97.27 million dollars.
  3. The same NPV without the event would be given by a rate of 10.35%, a premium of 0.35 percentage points.
  4. For comparison, a premium of 5 percentage points “for country risk”: NPV at 15% is 64.38 million dollars, which is 35.75 million less.
Answer: Accounting for the event explicitly reduces the expected NPV by 2.86 million dollars, which equals a premium on the rate of only 0.35 percentage points. A premium of 5 percentage points would take 35.75 million dollars.

What it means. A premium of 5 points would mean that the investor expects events more than ten times heavier than this, or counts the same thing twice. Besides, a premium hits the distant flows regardless of when and what may change (the premium and time). It is more reliable to list the events that really can happen, to estimate their probabilities and consequences, to put them into the flow or into a decision tree (Decision trees and the value of information), and to name in the conclusion what is left. The probability and the size of the change are assumed.

Changes of taxes are most often linked with the price: a windfall tax is introduced when oil is expensive. Then the regulatory risk cuts off exactly the good outcomes, and in a calculation with one price it is not seen at all.

Worked exampleA windfall tax at a random price
Given (assumed data)
Trials
the same 10,000 as in the example with the price models
Tax
from project year 5, half of the excess of the price over $60/bbl on each barrel; it reduces the base of the income tax (assumed)
Solution
  1. At a constant price of $50/bbl the tax is not paid: NPV stays at 100.1 million dollars.
  2. Random walk: the mean NPV 99.3→84.099.3 \to 84.0 million dollars; the high outcome P10 273→225273 \to 225; the low outcome P90, −41 and −41, does not change.
  3. Mean reversion: the mean NPV 99.9→94.399.9 \to 94.3; P10 180→164180 \to 164 million dollars.
  4. If the tax is introduced with a probability of 0.3, the expected NPV with the walk is 0.7⋅99.3+0.3⋅84.0=94.70.7\cdot99.3 + 0.3\cdot84.0 = 94.7 million dollars.
Answer: A windfall tax, invisible at a price of $50/bbl, reduces the mean NPV by 15.3 million dollars with a random walk and by 5.6 with mean reversion, without touching the bad outcomes.

What it means. The wider the spread of the price, the more the investor loses from the taxes that switch on at a high price. They work like an option on a price rise (the right to the gain from a rise) that has been sold to the state. So progressive taxes and stabilisation clauses are valued on the distribution of the price, not on one scenario (a good tax system). The data in this example are assumed for illustration.

Financial risk: debt, covenants, partners

A project can be financed with the shareholders' money or with debt. Debt is cheaper than equity (the shareholders' own money; see the cost of capital), but interest and repayment are paid on a schedule at any oil price. So debt is financial leverage: it raises the return of the shareholders when the project earns more than the rate on the loan, and it lowers the return when the project earns less.

The return on equity with debt
ROE=ROA+DE (ROA−rd)\mathrm{ROE} = \mathrm{ROA} + \frac{D}{E}\,(\mathrm{ROA} - r_d)
where:
  • ROE\mathrm{ROE}the return on equity for a year, fraction
  • ROA\mathrm{ROA}the return on all the investment: the profit before interest divided by all the capital, fraction
  • D/ED/Ethe ratio of debt to equity, —
  • rdr_dthe rate on the debt, fraction

Units: fractions; before income tax (with tax, both parts are multiplied by 1−T1 - T)

Holds when
  • the return on the investment does not depend on how it is financed
  • the rate on the debt is constant

At ROA>rd\mathrm{ROA} > r_d each dollar of debt brings the shareholders the difference, and at ROA<rd\mathrm{ROA} < r_d it takes the difference away. The spread of ROE is 1+D/E1 + D/E times the spread of ROA: debt raises the risk for the shareholders even if the project itself does not change.

The lender looks at something else: whether there will be enough money for the payments of each year. The main measure is the debt service coverage ratio (DSCR). It is the cash flow available for debt service (CFADS), which is the revenue minus operating costs and taxes, divided by the interest and repayment of the year. The loan agreement contains covenants: obligations of the borrower, for example to keep the DSCR not below 1.2–1.4. The level is set in the agreement, and it depends on the lender and the project. If a covenant is broken, the bank may forbid dividends, demand early repayment, or demand extra collateral (assets pledged to the bank).

The debt service coverage ratio
DSCRt=CFADStIt+At\mathrm{DSCR}_t = \frac{\mathrm{CFADS}_t}{I_t + A_t}
where:
  • CFADSt\mathrm{CFADS}_tthe flow of the year that is available for debt service: revenue minus operating costs, payments on revenue and taxes; the capital expenditure on building the project, paid by the loan and by the shareholders' money, is not subtracted, US$ million
  • It, AtI_t,\ A_tinterest and repayment of the principal in year tt, US$ million

Units: dimensionless

Holds when
  • we calculate it for each year (often for each half-year) and watch the lowest value, not the average.

DSCR = 1 means that the flow just covers the payments. Below 1, there is nothing to pay with without the shareholders' money.

Worked exampleA loan for a project: the return of the shareholders and the debt coverage
Given (assumed data)
Project
from the library's examples at a constant price of $35, $50 and $60/bbl
Loan
90 million dollars in the middle of year 2 (it covers the investment of that year), 8% a year, 5 equal payments in years 3–7 (assumed)
Simplification
the income tax is calculated with no deduction of interest (a deduction would improve the flow of the shareholders a little)
Solution
  1. The payment: 90⋅0.081−1.08−5=22.5490\cdot\dfrac{0.08}{1 - 1.08^{-5}} = 22.54 million dollars a year.
  2. At $50/bbl the flow of the shareholders is: −50; 0; 32.8−22.54=10.2632.8 - 22.54 = 10.26 in year 3, and so on. The IRR of the project is 29.6%, and the IRR of the equity is 44.2%.
  3. At $35 and $60/bbl, the IRR of the project is 13.3 and 38.7%, and of the equity 17.9 and 57.8%. The swing is 38.7−13.3=25.438.7 - 13.3 = 25.4 percentage points for the project and 57.8−17.9=39.957.8 - 17.9 = 39.9 points for the shareholders.
  4. At $35/bbl in year 3, the flow available for debt service is 35.52 million dollars. The shareholders pay for the completion of the development (20 million dollars), so their flow is 35.52−20−22.54=−7.0235.52 - 20 - 22.54 = -7.02 million dollars: they have to pay in 7.02 million dollars.
  5. The lowest DSCR is 52.8/22.54=2.3452.8/22.54 = 2.34 at $50/bbl and 35.52/22.54=1.5835.52/22.54 = 1.58 at 35. A covenant of 1.3 is broken at a price below $30.1/bbl. The break-even price of the project by NPV at 10% is $32.4/bbl.
Answer: Debt makes the return of the shareholders 1.6 times more sensitive to the price than the return of the project. At $35/bbl the loan is serviced (DSCR 1.58), but in the first year of production the shareholders pay in 7.02 million dollars.

What it means. While the project earns more than 8%, debt is good for the shareholders. When it earns less, debt hurts them (the curves on the chart cross near the rate of the loan). The lender is better protected: at a price from $30.1 to $31.7/bbl it gets its payments with the agreed margin, while the return of the shareholders is already below 10%. For the shareholders, debt adds one more risk, a liquidity risk (the risk of lacking cash when it is needed): extra payments in bad years and the threat of breaking a covenant. So the margin of the DSCR at a low price is checked in advance. The data in this example are assumed for illustration.

IRR of the project and IRR of the equity with a loan, against the oil price3035404550556065010203040506070Constant oil price, US$/bblIRR, %equityprojectloan rate 8%DSCR = 1.3

Two rising lines: the horizontal axis shows the oil price from 30 to 65 dollars per barrel, and the vertical axis shows IRR from 0 to 70 per cent. The line of the project rises from 7 per cent at 30 dollars to 43 at 65. The line of the equity is steeper: from 5 per cent at 30 dollars to 64 at 65. The lines cross near a price of 31 dollars, where both equal 8 per cent, the rate of the loan, shown by the horizontal dotted line. The vertical line marks the price 30.1.

CalculatedThe IRR of the example project and the IRR of its equity with a loan of 90 million dollars at 8%, against a constant oil price. The dotted line is the rate of the loan: above it, debt raises the return of the shareholders, and below it, debt lowers it. The vertical line is the price of $30.1/bbl, below which the DSCR covenant of 1.3 is broken.
  • The interest rate. With a floating-rate loan, the payments grow together with the market rates: a rise of the rate by 3 percentage points on a debt of 90 million dollars costs 2.7 million dollars a year extra. A fixed rate moves this risk to the lender for a fee.
  • Refinancing. If the loan is shorter than the project, it will have to be replaced by a new one, maybe in a year of low prices, when banks are cautious and charge more.
  • The currency of the debt. A dollar loan with dollar revenue is a natural protection. With revenue in tenge, a weaker tenge increases the debt in tenge.
  • Leasing. Leased plants are also a form of debt: the payments go into operating costs and bring the economic limit closer at a low price (to buy or to lease).

Partners. Fields are more often developed together, and each participant has its own cost of capital, tax position, attitude to risk and price forecast. A small partner needs quick money, a large one needs reserves for years, and a state company must also meet its plans for production and purchases. The same figures give them different NPVs. Disagreements delay decisions. A participant who has not paid its share of the costs on the operator's request (a cash call) puts the whole project at risk. A joint operating agreement sets in advance how the participants vote, who pays for the one who refuses, and how they leave the project (working interest and partnership).

How to allow for external uncertainty in a decision

Methods of allowing for market and regulatory uncertainty
Method
One price scenario
What it gives
simplicity, comparability of the company's projects
The pitfall
hides the spread; a “flat” nominal price is a fall in real terms
Method
Sensitivity and the break-even price
What it gives
the margin of safety against the price, the exchange rate and the tax (break-even values)
The pitfall
no probabilities and no links between the variables
Method
Consistent scenarios
What it gives
pictures of the future: the price together with costs, the exchange rate and taxes
The pitfall
no probabilities; extreme combinations are unlikely
Method
Simulation with price paths
What it gives
the distribution of NPV, the probability of a loss
The pitfall
the result depends on the price model and the volatility
Method
Decision tree and real options
What it gives
the value of flexibility: to wait, to expand, to stop
The pitfall
needs probabilities and decision rules
Method
Transfer of risk
What it gives
a hedge, contracts, stabilisation, insurance
The pitfall
it costs money and does not cover everything (the transfer of risk)

An NPV calculation with one scenario silently assumes that decisions are taken at once and forever. In reality a company can put off development until the price becomes clearer, start with a first phase and expand it if it goes well, or stop a field earlier at a low price. The right, but not the duty, to take a decision later, when more is known, is called a real option. Its value grows with uncertainty: the wider the spread of the price, the more is gained by the one who can avoid putting money into a bad outcome (Decision trees and the value of information).

The value of the possibility to wait
Vwait=p max⁡(0, NPVhi)+(1−p) max⁡(0, NPVlo)1+iV_{\text{wait}} = \frac{p\,\max(0,\ \mathrm{NPV}_{\text{hi}}) + (1 - p)\,\max(0,\ \mathrm{NPV}_{\text{lo}})}{1 + i}
where:
  • VwaitV_{\text{wait}}the value of the project today if the decision is put off by a year, US$ million
  • NPVhi, NPVlo\mathrm{NPV}_{\text{hi}},\ \mathrm{NPV}_{\text{lo}}the NPV of development a year later, with a high and a low price forecast, at the date of the decision, US$ million
  • ppprobability of the high forecast, fraction
  • iidiscount rate, fraction per year

Units: US$ million today

Holds when
  • in a year the uncertainty is resolved, and the decision is taken at the price then known
  • the right to wait exists: the contract and the regulation do not oblige us to start now; waiting does not reduce the reserves and does not give the market to competitors

It is worth building now only if NPVnow≥Vwait\mathrm{NPV}_{\text{now}} \ge V_{\text{wait}}. The difference Vwait−max⁡(0, NPVnow)V_{\text{wait}} - \max(0,\ \mathrm{NPV}_{\text{now}}) is the value of flexibility.

Worked exampleBuild now, or wait a year
Given (assumed data)
A small field
the NPV of development at the date of the decision is 3⋅(P−20)−853\cdot(P - 20) - 85 million dollars: 3 million bbl of discounted production after tax, $20 of costs and taxes per barrel, and 85 million dollars of investment (assumed)
Price
the long-term forecast today is $50/bbl; in a year it will become clear whether it is 60 or 40, with equal chances
Rate
10%
Solution
  1. Build now: 3⋅(50−20)−85=53\cdot(50 - 20) - 85 = 5 million dollars.
  2. Wait: at 60 dollars 3⋅40−85=353\cdot40 - 85 = 35, so we build; at 40 dollars 3⋅20−85=−253\cdot20 - 85 = -25, so we do not build. The value of waiting today: 0.5⋅35/1.1=15.910.5\cdot35/1.1 = 15.91 million dollars.
  3. The value of flexibility: 15.91−5=10.9115.91 - 5 = 10.91 million dollars. It is better to build at once only if the forecast is above $56.7/bbl.
  4. If in a year the forecast turns out 70 or 30 dollars: the value of waiting is 0.5⋅65/1.1=29.550.5\cdot65/1.1 = 29.55 million dollars, and the limit is $65.0/bbl.
Answer: It is better to wait: 15.91 million dollars against 5 for building at once, although the expected price in a year is the same, $50/bbl.

What it means. The value of waiting does not come from hoping for a rise of the price (the expected price has not changed). It comes from the right not to put money into a bad outcome. The wider the spread, the more valuable this right, and the higher the price at which it is worth building at once. But the right must exist. In Kazakhstan the contract obliges the subsoil user to carry out the work programme and the deadlines approved in the project documents (obligations of the subsoil user, deadlines in the documents), and waiting may cost fines or the area itself. In the same way we value the possibilities to expand a project or to stop it earlier. The data in this example are assumed for illustration.

Terms and symbols

Volatility σ\sigma
The standard deviation of the logarithmic returns of the price, brought to a year.
Price elasticity of demand
The relative change of consumption divided by the relative change of the price. For oil in the short term it is small.
Spot, forward, futures
The price of immediate delivery, the contract price of a future delivery, and the same price in a standard exchange contract.
Contango and backwardation
Contango is a forward curve that rises as the delivery date moves later. Backwardation is a forward curve that falls.
Differential
The premium or discount of the price of a grade or a delivery point to the benchmark.
Random walk and mean reversion
Price models. In a random walk the pushes stay forever. With mean reversion the deviation from the long-term level gradually fades.
Stabilisation clause
A condition of a contract or a law that protects the investor from changes of the rules that make its position worse.
Financial leverage
The use of debt. It raises both the average return and the spread of the return on equity.
DSCR and covenant
The DSCR is the flow available for debt service divided by the payments of the year. A covenant is the borrower's obligation to keep it not below an agreed level.
Real option
The right, but not the duty, to change a project later (to wait, to expand, to stop) when more is known.

Common mistakes and misconceptions

Wrong

“Let us take the price from futures: it is the market's forecast.”

In fact

A futures price is a price at which a deal can be made today. It contains the cost of storage and of money, the benefit of having the oil in hand, and a payment for risk. A futures contract can fix the price of part of the production. But it is not a forecast of the price for years, and for a model in constant prices it still has to be converted.

Wrong

“A volatility of 30% a year means that in 10 years the price can deviate by 300%.”

In fact

The spread grows as the root of time, not in proportion: with a random walk it is 30⋅10≈9530\cdot\sqrt{10} \approx 95% in logarithms, and with mean reversion it stops growing after a few years.

Wrong

“In the worst scenario the price is 30 dollars, the costs are 20% higher, the tenge is stronger, taxes are higher.”

In fact

Such a combination is almost impossible: when oil is cheap, services get cheaper, the tenge gets weaker, and the state is more likely to introduce tax breaks. We build a scenario as a consistent picture, and we set the links between the variables explicitly.

Wrong

“We will allow for the risk of changing taxes with a premium of 5 percentage points on the rate.”

In fact

A premium is linked neither with the probability, nor with the time, nor with the size of the change, and it hits the distant flows. In the example of the lesson an explicit event was worth a premium of only 0.35 percentage points. It is more reliable to list the possible changes, to estimate them and to put them into the flow.

Wrong

“The IRR of the project is 13%, more than the loan rate of 8%, so nothing threatens the shareholders.”

In fact

The shareholders get the flow after the payments on the loan. In a bad year they have to pay in, and if a covenant is broken, the bank may forbid dividends or demand early repayment. We check the flow of the shareholders and the margin of the DSCR at a low price.

In depth: advanced detail

Where the formulas come from: the root of time, the correction and the half-life

The root of time. The logarithm of the price over a year is the sum of nn independent returns over periods Δt=1/n\Delta t = 1/n. The variances of independent terms add up: σyr2=n σΔt2\sigma_{\text{yr}}^2 = n\,\sigma_{\Delta t}^2, so σyr=σΔtn\sigma_{\text{yr}} = \sigma_{\Delta t}\sqrt{n}. For the same reason, over tt years with a random walk vt=σ2tv_t = \sigma^2 t.

The correction −v/2-v/2. If XX is normally distributed with a mean of 0 and a variance vv, the mean of eXe^{X} is ev/2e^{v/2}, not 1: the high values of the exponential outweigh the low ones. If we multiply eXe^{X} by e−v/2e^{-v/2}, we get a multiplier with a mean of 1, so the expected price stays Pˉ\bar P. The median of the price is then Pˉ e−v/2\bar P\,e^{-v/2}, which is below the expected price, and the more so the larger the spread. In the example of the lesson, the median price of year 9 with a random walk is 50 e−0.2550\,e^{-0.25}, about $39/bbl.

The variance with mean reversion. From Xt=φXt−1+σεtX_t = \varphi X_{t-1} + \sigma\varepsilon_t with independent εt\varepsilon_t we get vt=φ2vt−1+σ2v_t = \varphi^2 v_{t-1} + \sigma^2, v0=0v_0 = 0. This is a geometric progression: vt=σ2(1+φ2+…+φ2(t−1))=σ2(1−φ2t)/(1−φ2)v_t = \sigma^2(1 + \varphi^2 + \ldots + \varphi^{2(t-1)}) = \sigma^2(1 - \varphi^{2t})/(1 - \varphi^2). As t→∞t \to \infty the variance tends to σ2/(1−φ2)\sigma^2/(1 - \varphi^2): at σ=0.25\sigma = 0.25 and φ=0.6\varphi = 0.6 it tends to 0.312520.3125^2.

The half-life. Without new pushes, the deviation after hh years is φhX0\varphi^{h}X_0. Half is left when φh=1/2\varphi^{h} = 1/2, that is h=ln⁡0.5/ln⁡φh = \ln 0.5/\ln\varphi. At φ=0.6\varphi = 0.6 this is 1.361.36 years. In the continuous form of the same model (the Ornstein–Uhlenbeck process) the speed of reversion is κ=−ln⁡φ\kappa = -\ln\varphi, and h=ln⁡2/κh = \ln 2/\kappa.

Why a forward can be below the spot price: the benefit of having the oil

Whoever holds oil in storage has something that the holder of a forward does not have: the possibility to sell or process it today, to keep a plant running, and to fulfil a contract when supply is disrupted. This benefit is called the convenience yield yy. With it, the forward price is written as FT=S0 e(r+u−y)TF_T = S_0\,e^{(r + u - y)T}, where uu is the cost of storage as a share of the price per year, and the rates are continuous. In ordinary times yy is small, and the curve is in a small contango. In a shortage yy is large, and the forward goes below the spot price. This is backwardation, and it is the steeper the sharper the shortage.

For a producer, a steep backwardation is a signal that the high price is temporary: the market is ready to pay much more for oil now than for oil in a few months. Investment decisions for years ahead are not taken at such a price.

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Check yourself

  1. 1

    The daily volatility of the oil price is 2%. What is roughly the yearly volatility, if there are 252 trading days in a year?

    1. A.about 504%
    2. B.about 2%
    3. C.about 32%
    4. D.about 24%
    Show the answer

    Correct answer: C. about 32%

    2⋅252=2⋅15.87≈31.72\cdot\sqrt{252} = 2\cdot15.87 \approx 31.7%: with independent returns, the standard deviation grows as the root of the number of periods. The answer 504% is a multiplication by 252 instead of the root, and 24% is a multiplication by 12 (as for monthly data).

  2. 2

    Oil futures: for the nearest month 72, in 3 months 69, in 6 months 66 US$/bbl. What is such a curve called, and what does it say?

    1. A.Contango: the storage is full
    2. B.Backwardation: oil is needed more now than later
    3. C.Nothing can be said from the curve
    4. D.Contango: the market expects the price to rise
    Show the answer

    Correct answer: B. Backwardation: oil is needed more now than later

    The prices fall as the delivery date moves later: this is backwardation. It means that more is paid for oil now than for oil later: the benefit of having it is above the cost of storage and of money. It is not a forecast of a fall of the price, but a price at which a deal can be made today.

  3. 3

    Why, at the same yearly volatility, does a random walk of the price give a much larger spread of the NPV of a project than mean reversion?

    Show the answer

    With a walk, each yearly push stays forever, and failures add up. The price can stay low or high for years, and the variance of the logarithm of the price grows in proportion to time. With mean reversion, the deviations fade, and the variance stops growing after a few years. NPV depends on the prices of all the production years, so with the walk its spread is much wider. In the example of the lesson the standard deviation is more than twice as large, and the probability of a loss is ten times larger.

  4. 4

    The cash flow available for debt service in the worst year is 39 million dollars; the interest and repayment of this year are 30 million dollars. The covenant requires a DSCR not below 1.4. Is it met?

    1. A.No: DSCR = 0.77
    2. B.Yes: DSCR = 1.3
    3. C.Yes: the flow is larger than the payments
    4. D.No: DSCR = 1.3, which is less than 1.4
    Show the answer

    Correct answer: D. No: DSCR = 1.3, which is less than 1.4

    DSCR=39/30=1.3<1.4\mathrm{DSCR} = 39/30 = 1.3 < 1.4: the covenant is broken, although the payments are covered. The lender may forbid dividends or demand measures. We must check the margin of the DSCR at a low price in advance.

  5. 5

    A company with a contract for oil production in Kazakhstan, concluded in 2020, fears a rise of taxes. Does the stability of conditions under the Subsoil Code protect it?

    Show the answer

    As a rule, no. The Code protects signed contracts from changes of legislation that make their position worse, but not in the field of taxation and a few other fields (Article 36). The tax terms of most contracts change together with the Tax Code. A stable tax regime is kept by production sharing agreements concluded before 2009 that passed the tax examination, and by contracts approved by the President. For contracts on complex projects, some norms of the Tax Code are applied in the version of the date of signing the contract (Article 756). Such a company must assess the risk of a change of taxes itself, with scenarios and probabilities.

  6. 6

    A project with an NPV of +4 million dollars can be started now, or in a year when it will be clear whether the price is high or low. In the bad outcome it will not be started. Why can waiting be worth more than 4 million dollars, even if the expected price does not change?

    Show the answer

    By waiting, the company puts money only into the good outcome and avoids the loss in the bad one. The value of waiting is the average of the positive NPV of the good outcome and the zero of the bad one, brought back by a year. With a wide spread of the price, it is larger than the NPV of the immediate decision averaged over the outcomes. This is a real option. It exists only if the contract and the regulation allow us to wait, and waiting does not cost the reserves or the area.

Updated: 19 October 2026