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Learning objectives: Describe and assess the major weakness attributable to single-factor approaches when hedging portfolios or implementing asset liability techniques. Define key rate exposures and know the characteristics of key rate exposure factors including partial ‘01s and forward-bucket ’01s. Describe key-rate shift analysis.


911.1. Suzanne the Risk Analyst is building an interest rate term structure and she is evaluating various candidate models. Her first candidate is Tuckman's Model 1 (aka, normally distributed rates and no drift) which has the advantage of extreme simplicity and is specified by (Tuckman 9.1): dr σ*dw. Her colleague Peter observes this is a single-factor model: the model's only factor is the short-term interest rate. Among the following, which is probably the strongest criticism against this model as a single-factor model? (Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011))

a. It compels us to assume yield to maturity (YTM) as the interest rate
b. A single-factor model incorporates yield volatility but cannot capture the convexity effect
c. It implies a parallel shift: if we shock the short rate by X basis points, it assumes all rates shock by X basis points
d. It necessarily must assume a perfectly flat term structure; aka, the flat yield curve assumption that is common for exams but unrealistic

911.2. Peter is a Financial Analyst whose boss asked him to develop a model, or if necessary a set of models, that are multi-factor risk models for the firm's fixed income and derivative investment portfolios. Specifically, there are four objectives as follows:

I. To measure and hedge the risk of bond portfolios in terms of the relatively small number of liquid bonds available, in particular, on-the-run government bonds
II. To measure and hedge the risk of a portfolio of swaps in terms of the highly liquid money market and swap instruments, which are more numerous
III. To measure the risk of mixed portfolios not terms of other securities but instead to model direct changes to the shape of the term structure
IV. To measure portfolio volatility by assuming a term structure of volatility but doing so without an excessive "curse of dimensionality;" i.e., avoiding too many correlation pairs

For these four objectives, Peter has three basic multi-factor risk metrics: key-rate exposures, partial '01s, and forward-bucket '01s. For which of the four objectives is key-rate exposures best suited?

a. I. only
b. III. only
c. I. and IV. only
d. I., II., III. and IV.; i.e., all four

911.3. Barbara is a Financial Analyst who is employing the key-rate exposure approach and she has decided that her model will include the following three specifications. First, there are four key rates: 2-, 5-, 10-, and 30-year. Second, the key rates are par yields (i.e., rather than spot rates or forward rates). Third, simple linear interpolation (as illustrated by Tuckman) is the rule for computing all other, non-key rates. Given these three decisions, which of the following statements is TRUE about her key rate exposure model?

a. If all four key rates are shifted simultaneously, the 20-year rate shifts one basis point (0.010)
b. If all four key rates are shifted simultaneously, the 20-year rate shifts one-half a basis point (0.0050)
c. The shift of the 10-year key rate (i.e., 10-year par yield) has no effect on the 30-year spot rate
d. Key rates (i.e., par yields) less than two years, and more than thirty years, are not shifted by definition of their exclusion

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