Why Oil’s Consumption Role Complicates Its Market Price of Risk

# Market Price of Risk for Consumption Asset - Hull's Example 28.1


# Market Price of Risk for Consumption Asset - Hull's Example 28.1












In Hull's Options, Futures, and Other Derivatives, he gives an example 28.1 as below.

> Consider a derivative whose price is positively related to the price of oil and depends on no other stochastic variables. Suppose that it provides an expected return of 12% per annum and has a volatility of 20% per annum. Assume that the risk-free interest rate is 8% per annum. It follows that the market price of risk of oil is (0.12-0.08)/0.2 = 0.2. Note that oil is a consumption asset rather than an investment asset, so its market price of risk cannot be calculated from equation (28.8) by setting mu equal to the expected return from an investment in oil and sigma equal to the volatility of oil prices.

I don't understand the bold paragraph. In particular,

- Why is that paragraph true? That is, why the market price of risk for oil cannot be calculate that way?

## Answer by Daneel Olivaw (score 1, accepted)

https://quant.stackexchange.com/a/51868

Note that just before Equation (28.9), Hull writes $-$ my emphasis:

> The market price of risk of [asset] $\theta$ measures the trade-offs between risk and return that are made for securities dependent on $\theta$.

Additionally, some lines below $-$ my emphasis:

> Chapter 5 distinguished between investment assets and consumption assets. An investment asset is an asset that is bought or sold purely for investment purposes by some investors. Consumption assets are held primarily for consumption.

You can view an investment asset solely as a stream of cash flows: you buy a stock because it will pay you a series of dividends as long as you hold it; you buy a bond because it pays coupons until it expires. There is nothing more you can do with those assets, they are purely financial in nature. Thus, the only trade-off between a stock and a bond is in terms of risk and return: do I want to buy into a stock, which has a better expected return than a bond, at the cost of taking greater risk? There are really no other considerations.

On the other hand, consider consumption assets such as oil and liquefied gas. These assets also have their own market and can be freely traded based on their prevailing price. You might view them as an investment, in which case you might also consider their risk/return profile. But other considerations come into play: they are also source of energy. Some market participants other than you might view them primarily as so, as hence the trade-offs are more complex: as an investment, you might prefer oil over gas because the risk/return profile is more attractive, but someone else might prefer gas over oil because they seek them for consumption and might consider gas is a more environmentally-friendly source of energy than oil, or have better capacity to store gas than oil, or whatever. So, even if gas has a lower return than oil and greater volatility, in which case the market price of risk calculated based on $\mu$ and $\sigma$ only will be much worse for gas than for oil, a buyer might nonetheless prefer gas over oil due to considerations other than financial.