CAPM GUIDED EXERCISES
PORTFOLIO BETA
You have a $48,000 portfolio consisting of Intel, GE, and Con Edison.
You put $20,000 in Intel, $11,200 in GE, and the rest in Con Edison.
Intel, GE, and Con Edison have betas of 1.3, 1, and .8, respectively.
What is your portfolio beta?
PORTFOLIO BETA
You have a $48,000 portfolio consisting of Intel, GE, and Con Edison.
You put $20,000 in Intel, $11,200 in GE, and the rest in Con Edison.
Intel, GE, and Con Edison have betas of 1.3, 1, and .8, respectively.
What is your portfolio beta?
(20/48)(1.3)+(11.2/48)(1.0)+(16.8/48)(0.8)=1.055
ARBITRAGE, SHORT & LONG
Consider the single factor APT. Portfolio A has a beta of 1.6 and an
expected return of 20%. Portfolio B has a beta of .7 and an expected
return of 16%. The risk-free rate of return is 9%. If you wanted to take
advantage of an arbitrage opportunity, you should take a short position
in portfolio __________ and a long position in portfolio _________.
Consider the single factor APT. Portfolio A has a beta of 1.6
and an expected return of 20%. Portfolio B has a beta of .7
and an expected return of 16%. The risk-free rate of return is
9%. If you wanted to take advantage of an arbitrage
opportunity, you should take a short position in portfolio
__________ and a long position in portfolio _________.
SHORT & LONG
0.20 –0.09
0.16 – 0.09
<
1.6
0.7
A
B
;Short A; Buy B
UNDERPRICE/FAIRLY PRICE/OVERPRICED?
Our opinion is that security A has an expected rate of return of 0.145. It
has a beta of 1.5. The risk-free rate is 0.04, and the market expected
rate of return is 0.11. According to the Capital Asset Pricing Model, this
security is:
UNDERPRICE/FAIRLY PRICE/OVERPRICED?
YOur opinion is that security A has an expected rate of return of 0.145.
It has a beta of 1.5. The risk-free rate is 0.04, and the market expected
rate of return is 0.11. According to the Capital Asset Pricing Model, this
security is UP/FP/OP ?
4% + 1.5 × (11% − 4%) = 14.5% = E(r)
FP?
UP/FP/OP – SHORT/LONG
• The risk-free rate is 5%. The expected market rate of return is 11%. If
you expect stock X with a beta of 2.1 to offer a rate of return of 15%,
you should:
UP/FP/OP – SHORT/LONG
• The risk-free rate is 5%. The expected market rate of return is 11%. If
you expect stock X with a beta of 2.1 to offer a rate of return of 15%,
you should:
5% + 2.1 × (11% − 5%) = 17.6% > 15% = E(r)
stock is overpriced and should be shorted.
PREMIUM
A stock generates a perpetual cash flow of $5 per share, per year. The
market index has an expected return of 11% and the risk-free rate is
3%. If the stock’s listed beta is 0.8 and I believe the true beta is 0.5,
how much of a premium will I pay for the stock?
PREMIUM
A stock generates a perpetual cash flow of $5 per share, per year. The
market index has an expected return of 11% and the risk-free rate is
3%. If the stock’s listed beta is 0.8 and I believe the true beta is 0.5,
how much of a premium will I pay for the stock?
rf + βlisted × [E(rm) − rf] = 3% + 0.8 × (11% − 3%) = 9.4%
→ P0 = $5 ÷ 0.094 = $53.19
rf + βtrue × [E(rm) − rf] = 3% + 0.5 × (11% − 3%) = 7.0%
→ P0 = $5 ÷ 0.07 = $71.43
Premium = $71.43 − $53.19 = $18.24