# EMSF

Topics: Treynor ratio, Stock, Sharpe ratio Pages: 11 (899 words) Published: September 3, 2014
﻿Ans 1:
Option A
Ans 2:
New Required return for HR = 7% + 2*(11% -7%) = 15%
New Required return for LR = 7% + .5*(11% - 7%) = 9%
So difference is 6%
Option E
Ans 3:
No of stocks = 20
Weight of each stock = 1/20
Beta of portfolio = 1.2
Beta of stock sold = 0.7
Beta of stock bought = 1.4
Hence new portfolio beta = 1.2 -.7/20 + 1.4/20 = 1.2 + .7/20 = 1.235 Option B
Ans 4:
New Beta = 0.7*1.5 = 1.05
Old required rate of return = 15%
So old risk free rate = 15% -5%*.7 =11.5%
New Required rate of return = 13.5% + 1.05*5% = 18.75%
Option C
Ans 5:
Security
Expected Return
Beta
Risk-free rate
Required rate of return
Difference
A
9.01%
1.7
7%
2%
10.40%
-1.39%
B
7.06%
0
7%
2%
7.00%
0.06%
C
5.04%
-0.67
7%
2%
5.66%
-0.62%
D
8.74%
0.87
7%
2%
8.74%
0.00%
E
11.50%
2.5
7%
2%
12.00%
-0.50%

So best option is security b
Ans 6:
Required return for Bradley =7% + 1.3*(12%-7%) =13.5%
Required return for Douglas = 7% + .7*(12% -7%) =10.5%
So difference is 3%
Option A
Ans 7:
Using regression we have
bX = 0.7358; bY = 1.3349.
rX = 7% + 5%(0.7358) = 10.679%.
rY = 7% + 5%(1.3349) = 13.6745%.
rp = 14/20(10.679%) + 6/20(13.6745%) = 11.58%

Option C
Ans 8:
Current Beta = 1.4*1/7 + 1*2/7 + .8*4/7 =.94
New Beta = 1.4*25/70 + .8*45/70 = 1.04
Hence increase in returns = 5.5%*1.04 – 5.5%*.94 = .39%
Option C
Ans 9:
Old portfolio beta = (12%-5.5%)/6% =1.08
New Beta = 1.08 + .3*.7 -.3*1.6 =.81
So Required rate of return = 5.5% + .81*6% =10.38%
Option B
Ans 10:
Expected return = 11%
Portfolio beta = (11% -5%)/6% =1
Or, .2*0 + x*1 + (.8 –x)*1.5 =1
Or, .8*1.5 -1 = .5*x
Or, x = .2/.5 = 40%
Option B
Ans 11:
Target Return = 12%
Current Beta= .2*.6 + .3*.8 + .3*1.2 + .2*1.4 = 1
So Market risk premium = (10%-5%)/1 = 5%
New Beta = (12% -5%)/5% =1.4
So .2*x + .3*.8 + .3*1.2 + .2*1.4 = 1.4
X = 2.6
Option e
Ans 12:

Mean return of portfolio = .75*2.7% + .25*(-1.9%) = 1.55%
The correlation is calculated using correlation function correl() in Excel Correlation = 0.56
Covariance = 0.56*16.9%*5.07% =.0048
Portfolio variance = .75^2*.0286 + .25^2*.00026 + 2*.0048*.75*.25 = 1.80% Ans 13:
Portfolio variance = 10*(.1*)^2*.1 = 1%
Option C
Ans 14:
For no arbitrage
(15% -rf)/B1 = (20% -rf)/B2
Or, (15%-rf)/(20%-rf) = B1/B2
Or, (15%-rf)/(20%-rf) = (Correlation between A and market* Std Dev of A)/(Correlation between B and market* Std Dev of B) As the two stocks are themselves perfectly correlated hence their correlation with market will also be same So,

(15%-rf)/(20%-rf) = 1%/2%
So, rf = 10%
Option E
Ans 15:
0 = w1^2* 10 + (1-w10^2)*40 + 2*w1*(1-w1)*sqrt(10)Sqrt(40)*(-1) Solving we have w1 = 66.67%
Option D
Ans 16:
Total portfolio variance = .1^2 * 10%*10 + 2*.1*.1*(-1/2)*sqrt(10%)*sqrt(10%) =.9% Option C
Ans 17:
Variance = (-1/1)^2 * 5 + (2/1)^2*10 -.8*2*2/1*sqrt(50) =22.37 Option D

Ans 18:
Variance of portfolio = (.2*.25)^2 + (.8*.05)^2 + 2*Correl*.2*.8*.25*.05 Or, .0050 = (.2*.25)^2 + (.8*.05)^2 + 2*Correl*.2*.8*.25*.05 Solving we have
Correlation = .225
Option D
Ans 19:
Option C
Ans 20:
Bond price = 60*(1-1.05^(-20))/.05 + 1000/1.05^20 =\$1124.62
Option E
Ans 21:
Financial calculator solution:
Inputs: N = 20; I = 6; PMT = 40; FV = 1,000.
Output: PV = -\$770.60; VB = \$770.60.
Number of bonds: \$2,000,000/\$770.60 = 2.596 bonds
Option B
Ans 22:
Bond price = C*(1-1.07^(-20))/.07 + 1000/1.07^20
Or, 1158.91 = C*(1-1.07^(-20))/.07 + 1000/1.07^20
C =\$85
Annual coupon rate = 85*2/1000 = 17%
Option D
Ans 23;
Current price of the bond = 1000/1.08^30 + 40*(1-1.08^(-30))/.08 =\$550 Option D
Ans 24:
Since the 1st bond sells at par hence Semi-annual YTM is half the coupon rate i.e. 4%. Annualized YTM = 1.04^2-1 = 8.16% Bond price of 2nd bond = 80*(1-1.0816^(-6))/.0816 + 1000/1.0816^6 =\$992.64 Option D

Ans 25:
We use excel to calculate YTM for the first bond
YTM = 12%
Bond Price for second one = 701.22
Or, C*(1 –(1.12)^(-5))/.12 +...