What is the (expected) risk-premium of the market?
What is the (expected) risk-premium of the stock?
FIN 300 - Risk and Return Pt. 3
15

CAPM Examples
Example 3 – Solution
R
i
= R
f
+
β
(R
mkt
– R
f
)
30% = 6% + 2
(R
mkt
– 6%)
24%/2 = 12% = R
mkt
– 6%
Return on Market
= 12% + 6% =
18%
Market Risk Premium
= 18% - 6% =
12%
Stock’s Risk Premium
= 30% - 6% =
24%
FIN 300 - Risk and Return Pt. 3
16

CAPM Examples
Example 4:
Given:
–
Stock has the same beta as the market
–
Market risk premium = 10%
–
Risk-free return = 4%
What is the (expected) return of the market?
What is the (expected) return of the stock?
What is the (expected) risk-premium of the stock?
What is the stock’s beta?
FIN 300 - Risk and Return Pt. 3
17

CAPM Examples
Example 4 – Solution
R
i
= R
f
+
β
(R
mkt
– R
f
)
Return on Market
= Mkt. Risk Premium + R
f
= 10% + 4% =
14%
Return on Stock = 14%; Same as Market
Stock’s Risk Premium
=
10%; Same as market
Stock’s beta =
1 (Beta of market =1)
FIN 300 - Risk and Return Pt. 3
18

Portfolio Beta
•
What if I have a portfolio of stocks with different
betas?
–
How can I calculate the beta of the overall
portfolio
–
Answer: I apply the same math as for the portfolio
return
•
Calculate a portfolio-weighted average beta
–
Multiply each beta by its portfolio weight
–
Sum up the terms and that is the portfolio
beta
FIN 300 - Risk and Return Pt. 3
19

Portfolio Beta Example
•
Invest $1M in a portfolio of assets
–
$200k invested in a stock with a beta = 0.4
–
$300k invested in a stock with a beta = 2
–
$100k invested in T-Bills (assumed to be risk-free)
–
$400k invested in a market index fund (assumed
to resemble the market portfolio)
•
What is the beta of the overall portfolio?
FIN 300 - Risk and Return Pt. 3
20

Portfolio Beta Example
Note:
–
Beta of the risk-free T-Bills = 0
–
Beta of the market index fund = 1 = market beta
Portfolio weights:
$200k/$1M = 0.20 = 20% in beta=0.4
$300k/$1M = 0.30 = 30% in beta=2
$100k/$1M = 0.10 = 10% in beta=0 (T-Bills)
$400k/$1M = 0.40 = 40% in beta=1 (Mkt)
Portfolio beta
= 0.20(0.4) + 0.30(2) + 0.10(0) + 0.40(1)
= 0.08 + 0.60 + 0 + 0.40 =
1.08
FIN 300 - Risk and Return Pt. 3
21

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- Olander
- Capital Asset Pricing Model, Corporate Finance, Ri, Return Pt.