238 PART 2 Important Financial Concepts
U.S. Treasury bills (T-bills)
Short-term IOUs issued by the
U.S. Treasury; considered the
risk-free asset.
TABLE 5.12 Austin Fund’s Portfolios
V and WPortfolio V Portfolio W
Asset Proportion Beta Proportion Beta1 .10 1.65 .10 .80
2 .30 1.00 .10 1.00
3 .20 1.30 .20 .65
4 .20 1.10 .10 .75(^5) . (^2) (^0) 1.25 . (^5) (^0) 1.05
Totals 1
.
0
0
1
.
0
0
risk-free rate of interest, RF
The required return on a risk-free
asset,typically a 3-month U.S.
Treasury bill.
EXAMPLE The Austin Fund, a large investment company, wishes to assess the risk of two
portfolios it is considering assembling—V and W. Both portfolios contain five
assets, with the proportions and betas shown in Table 5.12. The betas for the two
portfolios, bvand bw,can be calculated by substituting data from the table into
Equation 5.7:
bv(.101.65)(.301.00)(.201.30)(.201.10)(.201.25)
.165.300.260.220.2501.195 1
.
2
0
bw(.10.80)(.101.00)(.20.65)(.10.75)(.501.05)
.080.100.130.075.525.
9
1
Portfolio V’s beta is 1.20, and portfolio W’s is .91. These values make sense,
because portfolio V contains relatively high-beta assets, and portfolio W contains
relatively low-beta assets. Clearly, portfolio V’s returns are more responsive to
changes in market returns and are therefore more risky than portfolio W’s.
The Equation
Using the beta coefficient to measure nondiversifiable risk, the capital asset pric-
ing model (CAPM)is given in Equation 5.8:
kjRF[bj(kmRF)] (5.8)
where
kjrequired return on asset j
RFrisk-free rate of return, commonly measured by the
return on a U.S. Treasury bill
bjbeta coefficient or index of nondiversifiable risk for asset j
kmmarket return; return on the market portfolio of assets
The CAPM can be divided into two parts: (1) risk-free of interest, RF,which
is the required return on a risk-free asset,typically a 3-month U.S. Treasury bill
(T-bill), a short-term IOU issued by the U.S. Treasury, and (2) the risk premium.
These are, respectively, the two elements on either side of the plus sign in Equa-
tion 5.8. The (kmRF) portion of the risk premium is called the market risk pre-