Jan 08

The 2007 FRM. How to get a jump start: Part 2 (Market Module)

by David Harper, CFA, FRM, CIPM

FRM | Risk |

MarketRisk

As a reminder, this is a brief series on getting a head start, even before we know the assigned readings, on the 2007 FRM exam. In part one, I reviewed the essential building blocks of the Quantitative Module. Now consider Module II: Market Risk and Management. Last year, GARP moved several fixed income readings into this module; it has become a huge module.

At Bionic Turtle, our approach is to start with the fundamental building blocks. We believe this is the best way to learn new material. Unless there is a massive curriculum change, we'll assume the same building blocks for the Market Risk module:

MarketRiskBuildingBlocks

Notice I consider two concepts as foundational to the others: spot/forward rates and stochastic returns. After teaching this content for several years, I believe the biggest hurdles are the early hurdles. Immerse yourself in basics and advanced concepts becomes easier; skip the basics and you'll struggle. Many advanced concepts are merely the concatenation of several essential building blocks.

Therefore, take your time on basic elements like the calculation of a forward rate and the theories surrounding stochastic returns. If you can understand stochastic returns, the value at risk (VaR) concepts follow naturally. A deep and full understanding of the forward rate calculation, you might be surprised to learn, puts you halfway into the term structure of interest rates and even the Black-Scholes option pricing model.

In regard to the forward rates, we reduce several assigned readings to a single chart:

ForwardRate

Lacking market inefficiencies (namely, contango or normal backwardation),the forward price is equal to the estimated future spot price. And the future spot price is today's spot price projected forward in time but with the costs and benefits of ownership incorporated into the price.

What are the costs and benefits of asset ownership, that impact the expected future spot price? The four forces are illustrated in the arrows above. We?ll need to finance the asset, so the risk-free rate is the financing cost. (That's the second red up-arrow; it's up because it increases the expected future spot price and therefore the forward price.) Also, if it is a physical commodity like corn, we'll need to store the asset. That's a storage cost; economically the storage cost behaves like a financing cost; it increases the estimated future spot price.

On the other hand (and working in the opposite direction), if it's a financial asset (e.g., a basket of stocks), the owner of asset may receive income or dividends. The dividend yield is an offset to storage costs. Finally, the asset may confer convenience benefits that we call the convenience yield. For example, if our company uses gold as an input, it may be "convenience" to hold actual gold inventory. The convenience yield is the quantification of that benefit. These four forces conspire to set the price of the estimated future spot price, which equals the forward/futures price under an efficient market assumption.

You can get a head on this with the John Hull text, Chapters 2 through 5.

In regard to stochastic returns, Chapters 1 to 3 of the Linda Allen text are highly likely to repeat in the curriculum; her discussion of the stochastic behavior of returns helpful. The FRM exam, of course, is much ado about VaR. It is helpful therefore to get familiar with both the strengths and weaknesses of a parametric approach in which we make convenient assumptions about the nature of returns:

  • We often assume normality because, conveniently, normality only requires two parameters (mean and standard deviation)
  • Also, the central limit theorem tends to support our reliance on the normality assumption
  • But risk generally (and VaR specifically) is concerned about "left-tail losses:" the extreme left tail of the distributions where losses occur
  • And actual returns do not tend to be normal. They are fat-tailed (severe losses happen more often), skewed (declines tend to be more severe that upside jumps), and unstable (the most vexing: volatility like market conditions vary over time).

Normality is a human artifact. A convenience that lets us audaciously, and incorrectly, claim to describe returns with only two parameters. So after you see that, start examining the problem with it: actual returns are chaotic.

My recommendation on getting a head start in Market Risk is therefore, to study the Hull and Allen chapters. Make your goal a deep understanding of the cost-of-carry model (i.e., the model that solves for the price of the future/forward as a function of the expected future spot price) and the stochastic nature of returns with an emphasis on challenges (or weaknesses) in the typical normality assumption.

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