Sep 08

FRM 2008 Episode #13 (Traditional Investment Risk)

by David Harper, CFA, FRM, CIPM

FRM | |

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In this issue

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Every week I publish short (< 10 min) screencasts to give you a financial learning boost. Get your daily fix! Since the last newsletter, I recorded the following screencasts:

About Episode #13 (Investment Risk A)

We just published the latest screencast episode (Episode #13, Investment Risk A). This is the first screencast in the Invest Risk discipline. This screencast episode has a 91-page PowerPoint you can download in two parts (part 1= 50 min plus part 2 = 50 minutes). We continue to follow the sequence of GARP's 2008 FRM Study Guide. Please find links to the twelve previous episodes (#1 to #12) at the end of this note. After the next episode (#14, Investment Risk B), we will have finished the regular sessions and I will start cram session reviews. I will be sending you an email soon with information on the cram sessions!

Amenc on CAPM

cml

The capital asset pricing model (CAPM) is classic but please don't underestimate it. The theory (equilibrium) matters as much as the equation. Note CAPM "sets the stage" for the risk-adjusted performance metrics (RAPMs) and Grinold's performance attribution.

  • We can view the CAPM as a the prototypical single-factor model (singe factor = equity risk premium): excess return is a linear function of sensitivity to the factor. Several of the other models mentioned in the FRM are multi-factor generalizations: excess returns are a function of sensitivities to other factors. These are easier once we grasp the general form: excess return = [sensitivity to factor #1][factor #1] + [sensitivity to factor #2][factor #2] + .... + residual.
  • Grinold attributes active returns (i.e., portfolio returns minus benchmark) to a set of factors plus a specific (residual) term. The factors are divided into active systematic exposure and residual exposure to common factors (industry, risk index). Further, the active systematic returns are parsed into three components: expected active beta, active beta surprise, and active benchmark timing.
  • "However, according to CAPM, we expect a positive return here if the active beta is positive on average...The first component, based on the average active beta and the expected benchmark return, is not a component of active management."

Grinold's performance analysis

grinold

This reading, in my opinion, is difficult because the authors do not provide a step-by-step walk thru of the calculations. On the member page, I uploaded a spreadsheet example of the decomposition of the total active systematic return into its three components.

Jorion on Portfolio Risk

jorion7

I also replicated Jorion's example of a two-asset currency portfolio to illustrate the value at risk (VaR) concepts. I do recommend you look at this spreadsheet (see "2008 Invest: Portfolio VaR Analytics" on the member page).

In a few rows, I show the key metrics from Jorion:

  • Covariance matrix to give portfolio VaR
  • Individual VaRs
  • Marginal VaRs (both ways)
  • Beta
  • Component VaRs

Risk Budgeting

Aside from the qualitative AIMs/learning outcomes in this reading, the two topics are:

  • A pension fund will be concerned with funding risk. In this context, VaR becomes surplus at risk (SaR). But the idea is exactly the same: what is the worst expected loss over a period given some confidence level. The only difference is that instead of absolute VaR (i.e., loss relative to zero), we solve for loss relative to a zero surplus.
  • The budgeting of risk across active managers. The key idea, I think, here is that "relative risk budgets should be proportional to the information ratios."

New Learning Spreadsheets Added

learnxls

Since the last episode, I added several new learning spreadsheets to the member page:

  • Basel II standardized credit grid. This spreadsheet dynamically computes the capital charge if given the exposure type, size and rating
  • Basel II internal ratings based (IRB) approach to credit risk. Simple application of the capital charge employing the asymptotic single risk factor (ASRF) method used in IRB.
  • Illustration of correlation’s impact on portfolio returns/variance.
  • Security Market Line (SML) and Capital Market Line (CML). These are classic but try not to take them for granted. Like countless finance texts, I tried to illustrate both with the simplest possible assumptions (a two-asset portfolio)
  • Grinold’s Performance Analysis: This spreadsheet implements the (tough) last section of the FRM assigned Grinold Chapter 17. Given two input series (active portfolio beta and benchmark excess returns), this shows the deconstruction of total active systemic return into its three components (expected active beta, beta surprise, and benchmark timing
  • Risk-adjusted performance measures (RAPMs). Using the same SML (above), this illustrates Treynor, Sharpe, Jensen’s alpha, information ratio (IR) and the t-stat
  • Best hedge (Jorion Chapter 7). Simple, with graph proving the point.
  • Surplus at risk (Jorion Chapter 17)
  • Risk budgeting (Jorion Chapter 17)
  • Portfolio VaR Analytics (Jorion Chapter 7)

For the 2008 FRM exam, I have now uploaded 75 freshly constructed learning spreadsheets! Especially given that the exam is little more than two months away, I recommend you only refer to those that you need to plug a knowledge gap. As I am sure you know by now, on the member page, I highlighted in yellow the more critical subset. Of the 75, I have highlighted only 20.

Screencast Tutorial

Paid member access the screencast in the member section. In addition to the viewable screencast:

  • You can downloadable the underlying Power Point slides (in PDF format). For this episode, there is a single 91 page deck.
  • An ipod format (.m4v)
  • A downloadable version of the screencast in a .zip file. (Save to new directory on local and launch the .html file.)

Non-members can sample the start of the screencast tutorial here.

Practice Questions

As always, I wrote some engagement-type questions to provoke your thinking on the episode.

Question #1 (CAPM)

Assume the riskless rate is 4% and the expected return on the overall market portfolio is 10%. We want to analyze the performance of a portfolio. In regard to the portfolio, the expected return is 12% with volatility of 20% and beta of 1.2. The tracking error is 3%.

(i) What is the meaning of the "market portfolio" and what distinguishes the market portfolio from other portfolios on the efficient frontier?
(ii) What is the equity risk premium, the price of risk and the quantity of risk?
(iii) With this information, can we plot the CML and the SML?
(iv) What is the Treynor ratio and when would we use it?
(v) What is the Sharpe ratio and when would we use it?
(vi) What is Jensen's alpha and when would we use it?
(vii) What is the information ratio?
(viii) How many years of performance do we need to establish the portfolio's alpha is significant?

Question #2 (Performance Analysis)

In Grinold Chapter 17, Performance Attribution and Analysis deconstructs periodic returns into components ("attributes returns to components"). For example, if the portfolio return is 12% and the benchmark is 10%, then the ACTIVE RETURN is +2%. This active return is attributed to components.

(i) What are the components?
(ii) Which systematic and which are residual, and what do these terms mean?
(iii) Which are components of active management?
(iv) Where is skill captured?
(v) Where is luck captured?

Question #3 (Portfolio Risk)

Assume a $200 two-asset portfolio with equal positions in both assets ($100 + $100). Asset #1 has volatility of 10%, Asset #2 has volatility of 14%. Their correlation is 20%. Our desired confidence is 99%.

(i) What is portfolio volatility?
(ii) What is portfolio VaR and diversified VaR and what is the difference?
(iii) What are the individual VaRs?
(iv) What is the incremental VaR?
(v) What are the component VaRs and percentage contributions?
(vi) If correlation is perfect (1.0), how will portfolio VaR compare to individual VaRs?

Question #4 (Risk Budgeting)

The trustees for a pension fund need to allocate $100 million among two active managers and the benchmark. They want to maximize the information ratio subject to an overall tracking error volatility (TEV) of 3%. Manager #1 has a TEV of 5% with an information ratio (IR) of 0.5; Manager #2 has a TEV of 4% with an IR of 0.4. Optimization shows that the portfolio IR should be 0.64.

(i) With 99% confidence, what is the risk budget?
(ii) What is the TEV and IR of the benchmark index?
(iii) What are the managers' implied expected returns?
(iv) What is the optimal allocation?

My answers to these questions

Previous newsletters

Here are links to Episodes #1 through #13:

Thanks very much.

David-Harper_100w

David Harper, CFA, FRM, CIPM
Founder
www.bionicturtle.com

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