# EMSF

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

Risk Premium

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 +...

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