Multiple Linear Regression 71
have argued that hedge funds pursue strategies that have option-like (non-
linear) payoffs and this occurs even if an option strategy is not pursued.^19
Consequently, Dor and Jagannathan add four S&P 500 index strategies to
the 12 asset classes. This second regression, referred to as the “Basic Model
- Options Strategy,” shows that by adding the four option indexes, the R^2
increases significantly for each hedge fund.
Rich/Cheap Analysis for the Mortgage Market
Regression analysis has long been used to attempt to identify rich and cheap
sectors of the bond market. Here we will use a relative value regression
model developed by the Mortgage Strategy Group of UBS. The depen-
dent variable is the mortgage spread, a variable measured as the difference
between the current coupon mortgage^20 and the average swap rate. The
average swap rate is measured by the average of the 5-year swap rate and
10-year swap rate.
There are three explanatory variables in the model that have historically
been found to affect mortgage pricing:
- The level of interest rates
- The shape of the yield curve
- The volatility of interest rates
The level of interest rates is measured by the average of the 5-year swap
rate and 10-year swap rate. The shape of the yield curve is measured by the
spread between the 10-year swap rate and 2-year swap rate. The volatility
measure is obtained from swaption prices.
(^19) See Lawrence A. Glosten and Ravi Jagannathan, “A Contingent Claim Approach
to Performance Evaluation,” Journal of Empirical Finance 1 (1994): 133–160; Mark
Mitchell and Todd Pulvino, “Characteristics of Risk in Risk Arbitrage,” Journal of
Finance 56 (December 2001): 2135–2175; and William Fung and David A. Hsieh,
“The Risks in Hedge Fund Strategies: Theory and Evidence from Trend Followers,”
Review of Financial Studies 14 (2001): 313–341; Philip H. Dybvig and Stephen
A. Ross, “Differential Information and Performance Measurement using a Security
Market Line,” Journal of Finance 40 (1985): 383–399; and Robert C. Merton, “On
Market Timing and Investment Performance I: An Equilibrium Theory of Values for
Markets Forecasts,” Journal of Business 54 (1981): 363–406.
(^20) More specifically, it is what UBS calls the “perfect current coupon mortgage,”
which is a proxy for the current coupon mortgage.