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They will typically see the opportunity to apply what they consider to be

their superior acumen and make money by coming in between producers

and consumers. What is happening in all cases is that risk and reward are

being shared. Furthermore, if the result is that risks are taken by those who

are better placed to take them, then this does drive down the overall cost of

those risks to society.

Valuing financial options

Now until a relatively few years ago there was no agreed means of valuing a

financial option. This did not stop people who really wanted to from buying

or writing options. It did, however, greatly limit their use because the liquid-

ity of the market in options was limited to those prepared to trade despite

having no proven valuation method. Prices were set by supply and demand

pressures.

The standard approach of discounting forecast future cash flows was con-

sidered not to be suitable, for two reasons. These were that it was very diffi-

cult to forecast the expected cash flow associated with an option and it was

considered impossible to calculate the correct discount rate because the risk

inherent in an option changed over its life in an unpredictable way. The dif-

ficulty of forecasting cash flow was caused by the fact that the calculation

of expected value cash flow required one to assess the effect of high-impact

low-probability events. Whereas with a typical operating project one could

often ignore upsides on the grounds that they were offset by downsides, with

an option there was always either just an upside or just a downside.

474 Three views of deeper and broader skills

The discount rate represented an even greater problem. There was general

agreement that writing an option involved taking on more risks than sim-

ply owning the underlying asset. This indicated that the CoC for an option

would be higher than the CoC for owning the asset. The problem was that

the additional risk associated with an option would be a function of the asset

price and the strike price. Now our model for the asset price is that it will

vary like a random walk. This must in turn mean that the risk associated

with an option must also have a random nature and will change over the

period of the option. Hence, it is argued, the risk is not knowable and so the

CoC is incalculable.

My view about economic models is that if, for thousands of years, will-

ing buyers and willing sellers have been able to agree on a price yet the eco-

nomic value model appears not to work, one must simply conclude that the

economic value model is not the right approach to apply to this situation.

In 1973, Black and Scholes published their way of calculating the value of

an option. They approached the valuation problem through the principle

of arbitrage. One interpretation of this principle stated that if two courses

of action always produced the same result and if the prices of following both

courses are traded on the same market, then the price of following those two

courses of action must be identical. So if one could show that an option gave

exactly the same payout as something else, then the option must be worth the

same as that other thing.

Black and Scholes managed to show how, based on some quite realistic

assumptions, options on a share could be replicated by holding the right

combinations of shares and borrowing. Since both shares and borrowing can

be valued, options can be valued.

The reference to â€˜quite realistic assumptionsâ€™ is very important. If one were

prepared to accept some very simple models of future share price behaviour

one could come up with some equally simple options valuation formulae.

If, for example, one was prepared to accept that a future share would either

trade at one price or another and that the probability of each outcome was

known, the valuation would be trivial (our traditional valuation approaches

could cope!). Black and Scholes allowed for the fact that share prices were

continually changing in a random way and showed how it was still possible

to replicate a call option by a combination of share ownership and borrow-

ing, with the exact make-up of shares and borrowing changing continuously

in response to the market.

The exact formula looks (and is!) nicely complicated. Fortunately one does

not need to remember the formula. There are just five variables and these in

475 Second view: Valuing flexibility

turn need to be grouped into just two expressions. One can then either use

a preprogrammed computer function or a set of look-up tables to determine

the option value. The five variables are:

S The price of the asset today

E The exercise price for the option

Ïƒ The standard deviation per period of the rate of return on the asset

t The time to the exercise date of the option

r The risk-free interest rate

The two groupings that one calculates are:

Ïƒ Ã— âˆšt The standard deviation times the square root of the time to exercise.

S Ã· PV(E) The asset price divided by the present value of the exercise price.

Look-up tables will then reveal what the call option value is as a percentage of

the asset price today. The value of a put option is calculated by adding to the

call value the present value of the exercise price and subtracting the current

asset price.

Now most of the parameters in the formula are intuitive. What is not

immediately intuitive is the use of the risk-free rate and the fact that there is

no risk premium anywhere to be seen. The only risk factor is Ïƒ, the standard

deviation of the rate of return on the asset, and this works in such a way that

increased standard deviation increases call option value. This is a complete

contrast with the economic value approach where owning an asset that is

subject to higher risk lowers value. One can explain this by noting that it is

volatility that creates flexibility value. If there is no volatility there is no flexi-

bility and hence no flexibility value. Use of the risk-free rate is explained by

the fact that the approach is one which allows all risk to be removed. By con-

tinuously updating a portfolio of shares in the asset and borrowing one can

create an exact replica of the option. By replicating it one can cancel its risk.

The formula was quickly adopted by market participants and it facilitated

a large increase in the trade in so-called derivative products. The formula

became almost a self-fulfilling prophecy. People believe in it and so people

are willing to price options using it. A large influx of like-minded market

players creates exactly the liquidity that is necessary for a market to take off.

These investors are implicitly accepting the assumptions which were made

in deriving the formula. There are several, but the three key ones which I

476 Three views of deeper and broader skills

would highlight are that investors are prepared to make an estimate of future

volatility; to assume that markets are very liquid; and to ignore transaction

costs.

The question of volatility is of prime importance because it has a huge

impact on option value. It is never really safe simply to assume that past vola-

tility is a good indicator of future volatility and yet I do believe that many

investors implicitly do this. The more sophisticated investors certainly do not

and they will use anticipated changes in volatility compared with the historic

trend as a signal of whether to write or to buy options.

Liquidity is usually relatively unimportant, particularly for small invest-

ors. It can, however, become very significant, particularly if one is considering

very large positions. My view is that it is unreasonable to believe that there

will always be somebody prepared to do the opposite of what you want to do

once the scale of your investment becomes in any way material in relation

to the market overall. So I take the view that the valuation method becomes

more dangerous as the scale of investment increases. This provides quite a

dilemma for any individual or company that believes they have found a great

trading strategy to make money out of options. They must not overexploit it

or else they may become the victims of their own success when, all of a sud-

den, the market is not prepared to deal when they want to and prices change

in an unanticipated way.

Transaction costs need not really matter if investors are prepared to act

as though no arbitrage opportunities will exist. This would mean that prices

would remain where they â€˜oughtâ€™ to be without the need for some investors

to act in response to any opportunity. It does, however, cost money to put in

place the replicating portfolio which can allow investors to lock in any oppor-

tunity and so apparent mis-pricing of financial options can be sustained.

Can financial option valuation methods be used to value flexibility in projects?

The Nobel press release suggested that the answer to this question was â€˜yesâ€™.

The logic behind this was that the flexibility that existed in projects had many

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