Oct 05

Friday movie published: Investment Risk, Part 1

by David Harper, CFA, FRM, CIPM

FRM |

For members, the 1.5 hour tutorial reviews five groups of learning outcomes from the fifth and final module of the FRM. Two more movie tutorials will be published: Investment risk, Part 2 (e.g., hedge funds) on October 19th and a massive cram-session on November 2nd.

Today's tutorial includes the following (don't forget, the PowerPoint slides can be downloaded, they make good screen flashcards)

  • Portfolio risk (Jorion Chapter 7, Learning Outcomes 9.1 to 9.11)
  • VaR in investment management (Jorion Chapter 17. LOs 17.1 to 17.13)
  • Markowitz MPT (Stulz, LO 39.x))
  • Capital structure and risk (Stulz, LO 40.x)
  • Multifactor models (LO 41.x)

 

Some key ideas

What do the following have in common?

  • Option delta
  • Duration
  • Marginal value at risk (VaR)

They are all first derivatives! They are used to approximate a sensitivity (the change in price of an option given a change in stock price, the change in bond price given a change in yield, the change in portfolio VaR given a change in the 'component' position = marginal VaR). What is the difference between marginal VaR and incremental VaR? See graph below (from Jorion). Incremental VaR is the true answer: if we add/subtract an asset position, it gives the change in the portfolio VaR. But portfolio VaR is nonlinear. Ergo, incremental VaR is hard to get. Marginal VaR is the approximation of incremental VaR: not so accurate, but easy to calculate.

portfolioVaR

 

Jorion Chapter 7 is largely about the different priorities of different players. Within the investment industry, buy-side and sell-side tend to have different characteristics...

buyside

...and an important concept is funding risk. We tend to think of risk as volatility (standard deviation) or perhaps semi-variance. But a pension fund may be less concerned with volatility and more concerned with avoiding a shortfall: the assets fund liabilities.

 

Capital asset pricing model (CAPM)

Several learning outcomes refer to the capital asset pricing model (CAPM). The CAPM is a one-factor model, a subclass of the explicit (macroeconomic) multi-factor arbitrage pricing theory (APT) model.

capm

 

The CAPM has withstood some withering criticism over the years. It needs no defense. Peter Bernstein quotes Jack Treynor in Capital Ideas Evolving:

"One of the challenges to the CAPM is the idea that the market factor is not the only systematic factor in the market. However, the CAPM is utterly silent on whether there's one systematic factor in the market or two or three or ten. The CAPN still holds if there are other systematic factors, but it does say that if there are systematic factors they will have risk premiums that are proportional to the covariance with the market portfolio" - Jack Treynor, Capital Ideas Evolving

 

Stulz reduces to about two ideas

Stulz uses too many words, you have got two big ideas here:

  1. Shareholders won't pay for diversifiable (idiosyncratic) risk and
  2. Exceptions to the hedging irrelevance proposition (proposition: "hedging a risk does not increase firm value when the cost of bearing the risk is the same whether borne by the firm or by capital markets") are created by market imperfections.

An important "imperfection" is the cost of financial distress created by even the threat of bankruptcy.

whobearscost

 

Information ratio

The information ratio is a key measure: excess return (portfolio return minus benchmark) divided by tracking error:

informationratio

 

Multi-factor models

You need to skin the multi-factor models in a few ways:

  • Arbitrage (factors common to all securities; e.g., GDP) versus empirical (security specific factors like dividend yield)
  • Explicit (recognizable, observable. You can point to 'interest rates' as an explicit macroeconomic factor or 'earnings' as an explicit fundamental factor) versus implicit (endogenous or statistical)

The exogenous/endogenous distinction parallels the two credit risk approaches to estimating probability of default (PD). Reduced-form (or intensity-based) do not really analyze the default process. They focus on modeling a default that occurs at a random date. The look at variables "exogenous" to the company. On the other hand, structural models like the KMV Moody's approach, use endogenous variables. They use the firm' own market value (and volatility of same) to estimate the firm's own probability of default.

 

endogenous

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