Fin550 556 6. The following are the historic returns for the Chelle Computer Company: Year Chelle Computer General Index 1 37 15 2 9 13 3 -11 14 4 8 -9 5 11 12 6 4 9 Based on this information, compute the fo

profileFin-Acc-Boss
qweek_4_homework_.xlsx
Home>Business & Finance homework help>Fin550 556 6. The following are the historic returns for the Chelle Computer Company: Year Chelle Computer General Index 1 37 15 2 9 13 3 -11 14 4 8 -9 5 11 12 6 4 9 Based on this information, compute the fo

#6

6) The following are historic returns for the Chelle Computer Company:
Year Chelle Computer General index 
1 37 15
2 9 13
3 -11 14
4 8 -9
5 11 12
6 4 9
Compute the following: 
a) The correlation coefficient between Celle computer and the general index
b) The standard deviation for the company and the index 
c) The beta for the Celle Computer Company 
Solution:
Year Chelle General index
1 37 15
2 9 13
3 -11 14
4 8 -9
5 11 12
6 4 9
a) Correlation = 0.1305461489
b) SD (company) = 15.5649178175
SD (index) = 9.0553851381
c) Beta = 0.2243902439

#8

8) As an equity analyst, You have developed the following return forecasts and risk estimates for two different stock mutual funds. ( Fund T and Fund U).
Forecasted Return CAPM beta
Fund T 9.0% 1.20
Fund U 10.0 0.80
a) If the risk free rate is 3.9% and the expected market risk premium (i.e. E(Rm) –RFR) is 6.1% calculate the expected return for each mutual fund according to the CAPM.
b) Using the estimated expected returns from part A. along with your own return forecasts demonstrate whether Fund T and Fund U are currently priced to fall directly on the security market line (SML). Above the (SML) or below the (SML).
c) According to your analysts, are funds T and U overvalued, undervalued or properly valued. 
Solution:
a) Risk-free rate, rf = 3.90% Risk-free rate, rf = 3.90%
Market risk premium, RPm = 6.10% Market risk premium, RPm = 6.10%
Beta (T) = 1.2 Beta (U) = 0.8
Expected return (T) = 11.2200% Expected return (U) = 8.7800%
b) Since expected return is greater than forecasted return, the price is above SML.
Since expected return is less than forecasted return, the price is below SML.
c) Fund T is overvalued and fund U is undervalued.

#10

10) Draw the security market line for each of the following conditions 
a) (1) RFR= 0.08; Rm (proxy)=0.12
b) Rader Tire has the following results for the last six periods. Calculate and compare the betas using each index. 
Rates of Return 
Period Rader tire Proxy specific index True general index
1 29% 12 15
2 12% 10 13
3 -12% -9 -8
4 17% 14 18
5 20% 25 28
6 -5% -10 0
C) If the current period return for the market is 12% and for Rader Tire it is 11%. Are superior results being obtained for either index beta?
Solution:
a)
b) Period Radar Tire Proxy specific index True general index
1 29 12 15
2 12 10 13
3 -12 -9 -8
4 17 14 18
5 20 25 28
6 -5 -10 0
Covariance = 156.1666666667 147.00
Market variance = 244.5666666667
Beta = 0.64 0.60
c) Risk-free rate, Rf = 8% Risk-free rate, Rf = 8%
Market return, Rm = 12% Market return, Rm = 12%
Beta (proxy) = 0.64 Beta (true) = 0.60
Required return = 15.66% Required return = 15.21%
Rader’s performance of 11% would be inferior compared to either.

#3

3)
Factor Loading 
Stocks Mkt Macro Macro 2 
QRS 1.24 -0.42 0.00
TUV 0.91 0.54 0.23
WXY 1.03 -0.09 0.00
a) Calculate expected returns for the three stocks using just the MKT risk factor. Assume a risk free rate of 4.5%.
b) Calculate the expected return for the three stocks using all three risk factors and the same 4.5% risk free rate. 
c) Discuss the differences between the expected return estimates from the single factor model and those from the multifactor model. Which estimates are most likely to be more useful in practice?
d) What sort of exposure might Macro 2 represent? Given the estimated factor betas, is it really reasonable to consider it a common (i.e systematic) risk factor?
Solution:
3(a). RQRS = 4.5 +7.5x1.24
= 4.5 + 9.3
= 13.8% 13.80%
RTUV = 4.5 + 7.5x0.91
= 4.5 + 6.825
11.33%
RWXY = 4.5 + 7.5x1.03
12.23%
3(b). RQRS = 4.5 + 7.5x1.24 + (-0.3)x(-0.42) + 0.6x0.00
13.93%
RTUV = 4.5 + 7.5x0.91 + (0.3)x(0.54) + 0.6x0.23
= 4.5 + 6.825 – 0.162 + 0.138
= 11.301%
RWXY = 4.5 + 7.5x1.03 + (-0.3)x(-0.09) + ).6x0.00
= 4.5 + 7.725 + 0.027 + 0.00
= 12.252%
3(c). Assuming that the factor loadings are significant the three factor model should be more useful to the extent that the non-market factors pick up movements in returns not captured by the market return.
3(d). Because the factor loadings on MACRO2 are zero for two of the stocks, it appears that MACRO2 is not a systematic factor

#5

5) Suppose the three stocks (A, B, and C) and two common risk factors (1 and 2) have the following relationship: 
E(Ra)= (1.1)a1+(0.8)a2
E(Ra)=(0.7)a1+(0.6)a2
E(Rc)=(0.3)a1+ (0.6)a2
a) if a1= 4% and A2=2% what are the prices expected next year for each of the stocks? Aasume that all three stocks currently sell for $30 and will not pay a dividend in the next year. 
b) Suppose that you know that next year the prices for stocks A, B, and C will actually be $31.50, $35 and $30.50. Create and demonstrate a riskless, arbitrage investment to take advantage of these mispriced securities. What is the profit form your investment? You may assume that you can use the proceeds from any necessary short sale. 
Solution:
(a).
E(RA) = 1.1x0.04 + 0.8x0.02
0.06
= 0.06 or 6%
E(Price A) = $30(1.06) = $31.80
E(RB) = 0.7x0.04 + 0.6x0.02
0.292
= 0.04 or 4%
E(Price B) = $30(1.04) = $31.20
E(RC) = 0.3x0.04 + 0.4x0.02
0.128
= 0.02 or 2%
E(Price C) = $30(1.02) = $30.60
5(b). In order to create a riskless arbitrage investment, an investor would short 1 share od A and one share of C, and buy 2 shares of B. The weights of this portfolio are WA = -0.5, WB = +1.0, and WC = -0.5. The net investment is:
Short 1 share A $30
Buy 2 shares B ($60)
Short 1 share C $30
Net investment $0
The risk exposure is:
Risk Exposure Factor 1 Factor 2
A (-0.5)x1.1 (-0.5)x0.8
B (+1.0)x0.7 (+1.0)x0.6
C (-0.5)x0.3 (-0.5)x0.4
Net Risk Exposure 0 0
At the end of the period the profit is given by:
Profit = ($30 - $31.50) + 2x($35 – 30) + ($30 - $30.50)
= -$1.50 + $10 - $0.50
= $8

#7

Period Portfolio A Portfolio B Factor 1 Factor 2 Factor 2
1 1.08% 0.00% 0.01% -1.01% -1.67%
2 7.58% 6.62% 6.89% 0.29% -1.23%
3 5.03% 6.01% 4.75% -1.45% 1.92%
4 1.16% 0.36% 0.66% 0.41% 0.22%
5 -1.98% -1.58% -2.95% -3.62% 4.29%
6 4.26% 2.39% 2.86% -3.40% -1.54%
7 -0.75% -2.47% -2.72% -4.51% -1.79%
8 -15.49% -15.46% -16.11% -5.92% 5.69%
9 6.05% 4.06% 5.95% 0.02% -3.76%
10 7.70% 6.75% 7.11% -3.36% -2.85%
11 7.76% 5.52% 5.86% 1.36% -3.68%
12 9.62% 4.89% 5.94% -0.31% -4.95%
13 5.25% 2.73% 3.47% 1.15% -6.16%
14 -3.19% -0.55% -4.15% -5.59% 1.66%
15 5.40% 2.59% 3.32% -3.82% -3.04%
16 2.39% 7.26% 4.47% 2.89% 2.80%
17 -2.87% 0.10% -2.39% 3.46% 3.08%
18 6.52% 3.66% 4.72% 3.42% -4.33%
19 -3.37% -0.60% -3.45% 2.01% 0.70%
20 -1.24% -4.06% -1.35% -1.16% -1.26%
21 -1.48% 0.15% -2.68% 3.23% -3.18%
22 6.01% 5.29% 5.80% -6.53% -3.19%
23 2.05% 2.28% 3.20% 7.71% -8.09%
24 7.20% 7.09% 7.83% 6.98% -9.05%
25 -4.81% -2.79% -4.43% 4.08% -0.16%
26 1.00% -2.04% 2.55% 21.49% -12.03%
27 9.05% 5.25% 5.13% -16.69% 7.81%
28 -4.31% -2.96% -6.24% -7.53% 8.59%
29 -3.36% -0.63% -4.27% -5.86% 5.38%
30 3.86% 1.80% 4.67% 13.31% -8.78%
Portfolio A
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9852274077
R Square 0.9706730449
Adjusted R Square 0.9672891655
Standard Error 0.0099228067
Observations 30
ANOVA
df SS MS F Significance F
Regression 3 0.0847321843 0.0282440614 286.8521363361 4.89911143235997E-20
Residual 26 0.0025600144 0.0000984621
Total 29 0.0872921987
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 0.0056839482 0.0019475875 2.9184558912 0.0071672274 0.0016806248 0.0096872717 0.0016806248 0.0096872717
Factor 1 0.9906032205 0.0444732265 22.2741477901 1.83657576884391E-18 0.8991871941 1.0820192468 0.8991871941 1.0820192468
Factor 2 -0.2010465233 0.0435915428 -4.6120534065 0.0000935964 -0.2906502228 -0.1114428239 -0.2906502228 -0.1114428239
Factor 2 -0.133496714 0.0703726146 -1.8969980682 0.0689889279 -0.278149695 0.011156267 -0.278149695 0.011156267
Factor betas
Factor 1 0.9906032205
Factor 2 -0.2010465233
Factor 2 -0.133496714
Adj R2 0.967
Portfolio B
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9563845729
R Square 0.9146714512
Adjusted R Square 0.9048258494
Standard Error 0.0143192828
Observations 30
ANOVA
df SS MS F Significance F
Regression 3 0.0571461063 0.0190487021 92.9015281649 0
Residual 26 0.0053310884 0.0002050419
Total 29 0.0624771947
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 0.00692855 0.0028105008 2.4652367572 0.0206124501 0.0011514828 0.0127056171 0.0011514828 0.0127056171
Factor 1 0.9620466867 0.0641778813 14.9903154761 0 0.8301271625 1.0939662109 0.8301271625 1.0939662109
Factor 2 0.0459856945 0.0629055518 0.7310275988 0.4712995082 -0.0833185191 0.1752899081 -0.0833185191 0.1752899081
Factor 2 0.3190788392 0.1015524543 3.1420101208 0.0041580147 0.1103347798 0.5278228987 0.1103347798 0.5278228987
Factor betas
Factor 1 0.9620466867
Factor 2 0.0459856945
Factor 2 0.3190788392
Adj R2 0.90
For both regressions, the adjusted R2 are high i.e. (0.967 and 0.904 for portfolios A and B respectively. This imples that
the factor models explains more than 90% of the variation in each porfolio returns.
Factor 1 is the most likely factor to be a market factor. This is because it has a large, postive, and signficant effect on the both portfolios.
Factor 2 and factor 3 have different signs in both regressions.
A postive HML factor loading implies a value-oriented portfolio or stock. Portfolio B has a positive
loading on this factor, and hence is the more likely factor for the value-oriented portfolio.
Portfolio A has a negative loading on this factor, and as such it's more likely factor to be a growth-oriented portfolio.