Drag

# 作业代写｜Online Quiz Lecture 5 SOLUTIONS

## Overtime

1. You’re a global investor, and there are four well- diversified portfolios (A to D) and four systematic risk factors (1 to 4). For each portfolio, you know the beta to each risk factor, b1 through b4. There is also a risk- free bond. Assume that the APT holds for all portfolios and the risk free bond.

Portfolio b1 b2 b4 E[r]
A (Global Market Index) 1.0 0.0 0.0 0.0 27%
B (US Market Index) 1.0 0.0 0.0 17%
C (US Large Capitalization Index) 0.0 1.2 1.0 0.025%
D (US Small Capitalization Index) 0.4 1.2 1.5 0.5 37% Risk- free bond _ _ _7%

(a) Fill in the blanks in the table above.
all 0’s!

(b) Can you guess the sources of risk (or at least likely candidates) for each of the
first two factors by observing b1 and b2?
Factor 1 would be global economy and factor 2 would be the US economy prob-
ably.

(c) If you took a typical foreign stock and regressed it against one of the factors at
a time, which factor (1, 2, 3, or 4) would likely produce the highest R2?
Factor 1!

(d) Find the expected return on portfolio E, which has b1 =0.0,b2=0.2, b3= 1.0, and b4 = 0.0.

Portfolio b1 b2 b3 b4 E[r]-rf E[r]
C 0.0 1.2 1.0 0.0 18% 25%
B 0.0 1.0 0.0 0.0 10% 17%
T-Bill _ _ _0% 7%
C- B 0.0 0.2 1.0 0.0 8%
So E(rc)- E(rB)= 25- 17= 8%. That means E(rE)=8+7= 15%.

(e) Can you find all four lambda’s, the factor risk premiaλ1 …λ?

i. Portfolio A saysλ1 is 20%.
27%= 7%+ 1.0λ1

ii. Portfolio B saysλ2 is 10%.
17%= 7% + 1.0λ2

ii. To getλ3 = 6%, solve:

25%=7%+0X1+1.2λ2+1.0λ3+0.0λ4
25=7+1.2X10+λ3

iv. That leaves λ4 = 2% when we solve:

37% = 7% + 0.4λ1 + 1.2λ2 + 1.5X3 + 0.5λ4
37=7+0.4×20+1.2X10+1.5X6+0.5X4
Notice that once you know all four lambda ‘s, you can compute the expected return of any portfolios, if you are provided the betas involved.
2. 1.5λ1 = 10.5% givesλ1=7%.
1.5λ2 = 6% givesλ2=4%.
Under the APT, B should have 1.2*7% + 0.8*4% = 11.6%.
However, B has expected return of 11.2%, so the expected return sits below the APT SML，which means B is overpriced.