Multifactor Models
9-207-056
JANUARY 28, 2007
MALCOLM BAKER
Multifactor Models
There are two parts to this exercise. The first is to evaluate the performance of four mutual funds.
And, the second is to estimate the cost of capital for two firms.
Benchmarking
Both parts of the exercise are about choosing an appropriate benchmark, either for evaluating past investment returns or assessing a new project. Ideally, a benchmark should reflect the opportunity cost, or the best alternative investment. If an investment manager’s past returns significantly exceed an appropriate benchmark, then we can conclude that he or she had legitimate stock picking skill.
Similarly, if the expected return on a new investment project exceeds an appropriate benchmark, then we can conclude that it is worth undertaking.
In 1998, the SEC required all mutual funds to designate a benchmark to present alongside historical returns. The vast majority of equity funds use one of the following benchmarks: S&P 500,
Russell 1000 or Large Cap Value, Russell 1000 or Large Cap Growth, S&P Mid Cap 400, Russell Mid
Cap, Russell Mid Cap Growth, Russell Mid Cap Value, S&P Small Cap 600, Russell 2000, Russell 2000 or Small Cap Growth, or Russell 2000 or Small Cap Value.1 (Monthly returns on these portfolios, on the value-weighted market, on long-term government bonds, and on Treasury bills are shown in
Exhibit 1 for the period from January 2000 through December 2004.)
Academic research also provides some guidance on appropriate benchmarks. For example, under the assumptions of the capital asset pricing model (CAPM), diversified investors use the following formula to benchmark performance:
R f + β (Rm − R f ) , where Rf refers to the risk-free rate of return; Rm—Rf refers to the return on the market portfolio in excess of the risk-free rate; and β is the slope coefficient in a regression of firm or fund returns in excess of the risk free rate on Rm—Rf. This model can be used either prospectively, with expectations of future
JANUARY 28, 2007
MALCOLM BAKER
Multifactor Models
There are two parts to this exercise. The first is to evaluate the performance of four mutual funds.
And, the second is to estimate the cost of capital for two firms.
Benchmarking
Both parts of the exercise are about choosing an appropriate benchmark, either for evaluating past investment returns or assessing a new project. Ideally, a benchmark should reflect the opportunity cost, or the best alternative investment. If an investment manager’s past returns significantly exceed an appropriate benchmark, then we can conclude that he or she had legitimate stock picking skill.
Similarly, if the expected return on a new investment project exceeds an appropriate benchmark, then we can conclude that it is worth undertaking.
In 1998, the SEC required all mutual funds to designate a benchmark to present alongside historical returns. The vast majority of equity funds use one of the following benchmarks: S&P 500,
Russell 1000 or Large Cap Value, Russell 1000 or Large Cap Growth, S&P Mid Cap 400, Russell Mid
Cap, Russell Mid Cap Growth, Russell Mid Cap Value, S&P Small Cap 600, Russell 2000, Russell 2000 or Small Cap Growth, or Russell 2000 or Small Cap Value.1 (Monthly returns on these portfolios, on the value-weighted market, on long-term government bonds, and on Treasury bills are shown in
Exhibit 1 for the period from January 2000 through December 2004.)
Academic research also provides some guidance on appropriate benchmarks. For example, under the assumptions of the capital asset pricing model (CAPM), diversified investors use the following formula to benchmark performance:
R f + β (Rm − R f ) , where Rf refers to the risk-free rate of return; Rm—Rf refers to the return on the market portfolio in excess of the risk-free rate; and β is the slope coefficient in a regression of firm or fund returns in excess of the risk free rate on Rm—Rf. This model can be used either prospectively, with expectations of future