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1.The following are monthly percentage price changes for four market indexes.

Month DJ SP500

1 0.03 0.02 2 0.07 0.06 3 −0.02 −0.01 4 0.01 0.03 5 0.05 0.04 6 −0.06 −0.04

Russ500 Nicky

0.04 0.04 0.10 −0.02 −0.04 0.07 0.03 0.02 0.11 0.02 −0.08 0.06

(17 points) Compute the following.

a. Average monthly rate of return for each index

b. Standard deviation for each index

c. Covariance between the rates of return for the following indexes:

DJ– SP 500 SP500–Russ500 SP500–Nicky Russ500–Nicky

d. The correlation coefficients for the same four combinations

2.Xpord University has 10 million rupees in its consolidated fund. Xpord has hired your investment firm to manage the above fund. You work in the bond research department of the investment firm. And suppose that the portfolio manager has asked you to evaluate several bonds for potential purchase. Issuer Maturity Bond Rating Bond Annual Frequency of Coupon Coupon Payment Rate A 5% Annual B 8% Annual ? 6% Annual D 9% Semi- Annual Government Corporate Corporate Corporate S 5 3 4 Market Price (Rs.) 800 870 895 930 BBB AAA BB The economic team of your investment firm has updated its economic forecasts for the next five years and those details are given below. • Real risk-free rate :1% • Annual average of expected inflation rate for the next 5 years: 1% • AAA- Default risk premium:1% • BBB-Default risk premium: 2% • BB- Default risk premium: 3% • AAA-Liquidity risk premium: 0.6% • BBB-Liquidity risk premium :1% • BB-Liquidity risk premium :1.8% • Treasury Liquidity premium: 0% Maturity risk premium: 0.8 % per year The required rate of return will be calculated using following formula; Required rate of return = Real risk-free rafe + Inflation Premium + Default Risk Premium + Liquidity premium + Maturity Risk Premium The firm calculates the Inflation Premium based on following formula: Inflation Premium = (1-1) * Annual average of expected inflation Where, T-Maturity period in years
? The required rate of return will be calculated using following formula; Required rate of return = Real risk-free rate + Inflation Premium + Default Risk Premium + Liquidity premium + Maturity Risk Premium ? The firm calculates the Inflation Premium based on following formula; Inflation Premium = (T-1) * Annual average of expected inflation Where, T = Maturity period in years You can assume that the face value of bonds A, B, C and D is Rs.1000/= You are required to analyze the bonds and answer the following questions; i. The portfolio manager wants you to analyze above bonds and complete the following table (show all calculations). Further you are required to recommend witch bond/s to buy. Bond Current yield Require rate of Yield to Intrinsic value return maturity A B ? D ii. The portfolio manager is worried that the economy may enter a recession in 2021 with the covid -19 situation. Which bond would have the least risk in this scenario? Which bond would have the most risk? Why? The portfolio manager has asked you to identify any bonds that minimize the Reinvestment Risk. Which bond do you select? Justify your selection.

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Month	DJ	SP500	Russ500	Nicky
1	0.03	0.02	0.04	0.04
2	0.07	0.06	0.10	-0.02
3	-0.02	-0.01	-0.04	0.07
4	0.01	0.03	0.03	0.02
5	0.05	0.04	0.11	0.02
6	-0.06	0.04	-0.08	0.06

a) Average monthly rate of return for each index

Average monthly rate of return of DJ = (0.03+0.07-0.02+0.01+0.05-0.06)/6 = 0.0133

Average monthly rate of return of SP500 = (0.02+0.06-0.01+0.03+0.04+0.04)/6 = 0.0300

Average monthly rate of return of Russ500 = (0.04+0.10-0.04+0.03+0.11-0.08)/6 = 0.0267

Average monthly rate of return of DJ = (0.04-0.02+0.07+0.02+0.02+0.06)/6 = 0.0317

b) Standard deviation for each index

As the distribution is Sample, Stock’s Standard Deviation = √{1/(n-1)*∑(R_i-R_mean)²}

where, R_i is expected return of index i

R_mean is arithmetic mean of return

n is number of observation

Std dev of DJ:

Expected Return (%)R(i)	R(mean)	R(i)-R(mean)	{R(i)-R(mean)}²
0.03	0.0133	0.0167	0.00028
0.07	0.0133	0.0567	0.00321
-0.02	0.0133	-0.0333	0.00111
0.01	0.0133	-0.0033	0.00001
0.05	0.0133	0.0367	0.00134
-0.06	0.0133	-0.0733	0.00538

Stock’s Standard Deviation = Square root of{sum [{R(i)-R(mean)}²] / (n-1)} = Square root (0.0113/5) Stock’s Standard Deviation of DJ = 0.0476

Std dev of SP500:

Expected Return (%)R(i)	R(mean)	R(i)-R(mean)	{R(i)-R(mean)}²
0.02	0.0300	-0.0100	0.00010
0.06	0.0300	0.0300	0.00090
-0.01	0.0300	-0.0400	0.00160
0.03	0.0300	0.0000	0.00000
0.04	0.0300	0.0100	0.00010
0.04	0.0300	0.0100	0.00010

Stock’s Standard Deviation = Square root of sum [{R(i)-R(mean)}²] / (n-1) = Square root of (0.0028)/5 Stock’s Standard Deviation of SP500 = 0.0237

Std dev of RUSS500:

Expected Return (%)R(i)	R(mean)	R(i)-R(mean)	{R(i)-R(mean)}²
0.04	0.0267	0.0133	0.00018
0.10	0.0267	0.0733	0.00538
-0.04	0.0267	-0.0667	0.00444
0.03	0.0267	0.0033	0.00001
0.11	0.0267	0.0833	0.00694
-0.08	0.0267	-0.1067	0.01138

Stock’s Standard Deviation = Square root of sum [{R(i)-R(mean)}²] / (n-1) = Square root of (0.0283)/5 Stock’s Standard Deviation of Russ500 = 0.0753

Std dev of Nicky:

Expected Return (%)R(i)	R(mean)	R(i)-R(mean)	{R(i)-R(mean)}²
0.04	0.0317	0.0083	0.00007
-0.02	0.0317	-0.0517	0.00267
0.07	0.0317	0.0383	0.00147
0.02	0.0317	-0.0117	0.00014
0.02	0.0317	-0.0117	0.00014
0.06	0.0317	0.0283	0.00080

Stock’s Standard Deviation = Square root of sum [{R(i)-R(mean)}²] / (n-1) = Square root of (0.0053)/5 Stock’s Standard Deviation of Nicky = 0.0325

c) Covariance between the rates of return for the following indexes:

Cov (i,j) = √[1/(n-1)*∑{(X_i-X_mean)* (Y_j-Y_mean)}]

where, X_i is expected return of index i

X_mean is arithmetic mean of return of index i

Y_i is expected return of index j

Y_mean is arithmetic mean of return of index j

n is number of observation

DJ– SP 500

Expected Return (%) X(i)	X(mean)	X(i) - X(mean)	Expected Return (%) Y(j)	Y(mean)	Y(j) - Y(mean)	{X(i) - X(mean)}*{Y(j) - Y(mean)}
0.03	0.0133	0.01667	0.02	0.0300	-0.01000	-0.000167
0.07	0.0133	0.05667	0.06	0.0300	0.03000	0.001700
-0.02	0.0133	-0.03333	-0.01	0.0300	-0.04000	0.001333
0.01	0.0133	-0.00333	0.03	0.0300	0.00000	0.000000
0.05	0.0133	0.03667	0.04	0.0300	0.01000	0.000367
-0.06	0.0133	-0.07333	0.04	0.0300	0.01000	-0.000733

Cov(DJ, SP500) = sum [{X(i)-X(mean)}*{Y(j)-Y(mean)}] / (n-1) = (0.0025)/5

Cov(DJ, SP500) = 0.0005

SP500–Russ500

Expected Return (%) X(i)	X(mean)	X(i) - X(mean)	Expected Return (%) Y(j)	Y(mean)	Y(j) - Y(mean)	{X(i) - X(mean)}*{Y(j) - Y(mean)}
0.02	0.0300	-0.01000	0.04	0.0267	0.01333	-0.000133
0.06	0.0300	0.03000	0.10	0.0267	0.07333	0.002200
-0.01	0.0300	-0.04000	-0.04	0.0267	-0.06667	0.002667
0.03	0.0300	0.00000	0.03	0.0267	0.00333	0.000000
0.04	0.0300	0.01000	0.11	0.0267	0.08333	0.000833
0.04	0.0300	0.01000	-0.08	0.0267	-0.10667	-0.001067

Cov(SP500–Russ500) = sum [{X(i)-X(mean)}*{Y(j)-Y(mean)}] / (n-1) = (0.0045)/5

Cov(SP500–Russ500) = 0.0009

SP500–Nicky

Expected Return (%) X(i)	X(mean)	X(i) - X(mean)	Expected Return (%) Y(j)	Y(mean)	Y(j) - Y(mean)	{X(i) - X(mean)}*{Y(j) - Y(mean)}
0.02	0.0300	-0.01000	0.04	0.0317	0.00833	-0.000083
0.06	0.0300	0.03000	-0.02	0.0317	-0.05167	-0.001550
-0.01	0.0300	-0.04000	0.07	0.0317	0.03833	-0.001533
0.03	0.0300	0.00000	0.02	0.0317	-0.01167	0.000000
0.04	0.0300	0.01000	0.02	0.0317	-0.01167	-0.000117
0.04	0.0300	0.01000	0.06	0.0317	0.02833	0.000283

Cov(SP500–Nicky) = sum [{X(i)-X(mean)}*{Y(j)-Y(mean)}] / (n-1) = (-0.0030)/5

Cov(SP500–Nicky) = -0.0006

Russ500–Nicky

Expected Return (%) X(i)	X(mean)	X(i) - X(mean)	Expected Return (%) Y(j)	Y(mean)	Y(j) - Y(mean)	{X(i) - X(mean)}*{Y(j) - Y(mean)}
0.04	0.0267	0.01333	0.04	0.0317	0.00833	0.000111
0.10	0.0267	0.07333	-0.02	0.0317	-0.05167	-0.003789
-0.04	0.0267	-0.06667	0.07	0.0317	0.03833	-0.002556
0.03	0.0267	0.00333	0.02	0.0317	-0.01167	-0.000039
0.11	0.0267	0.08333	0.02	0.0317	-0.01167	-0.000972
-0.08	0.0267	-0.10667	0.06	0.0317	0.02833	-0.003022

Cov(Russ500–Nicky) = sum [{X(i)-X(mean)}*{Y(j)-Y(mean)}] / (n-1) = (-0.01027)/5

Cov(Russ500–Nicky) = -0.0021

d) The correlation coefficients for the same four combinations

Correlation coefficient between the two stocks = Covariance / Product of standard deviations = Cov (RA , RB) / (sigmaA x sigmaB )

where, A is one index

B is other index

sigmaA is std dev of A

sigmaB is std dev of B

DJ– SP 500

Correlation coefficient = Cov(DJ– SP 500)/ (std dev of DJ * std dev of SP500 )

= 0.0005 / (0.0476*0.0237) = 0.4432

SP500–Russ500

Correlation coefficient = Cov(SP500–Russ500)/ (std dev of SP500 * std dev of Russ500 )

= 0.0009 / (0.0237*0.0753) = 0.5043

SP500–Nicky

Correlation coefficient = Cov(SP500–Nicky)/ (std dev of SP500 * std dev of Nicky )

= -0.0006 / (0.0237*0.0325) = -0.7790

Russ500–Nicky

Correlation coefficient = Cov(Russ500–Nicky)/ (std dev of Russ500 * std dev of Nicky )

= -0.0021 / (0.0753*0.0325) = -0.8581

2.Given: We have assumed face value of all the bonds be Rs 1000

For Current Yield= (Coupon Payment)/Current Market price of the Bond

Yield to Maturity(YTM)= (Coupon+(Face Value-Market value)/maturity)/(Face Value-Market Value/2)

YTM for semi annual coupon payments= (Coupon/2+(Face Value-Market value)/maturity*2)/(Face Value-Market Value/2)

n= maturtiy period

C= Coupon payment

Given:

Required rate of return = Real Risk-Rree Rate+Inflation premium+Default Risk Premium+Liquidity Premium+Maturity Risk premium

Calculation as folllows:

Answer 1)

Answer2) a)The Bond A which is the government bond has the least risk

Reason: We do not have default risk premium for this bond which means it has no probability of default thus it is safeguarded from market risk also the government bonds are assumed to be the safest among the categories of bonds.

b)The Bond D has the highet risk

Reason: The credit rating of Bond D is also not good compare to other bonds and we have the highest default risk premium for this bond which means the probability of default on this bond is high. So, if we enter the recession the market will not favour the company which has issued the Bond D.

Default risk premium is the additional amount that we receive for the bond

Answer3) In this scenario, I would select the Bond C.

Reason: Though the yield of the Bond C is lesser than the Bond B and Bond D, the Bond C bond has the good credit rating with low liquidity premium which means the bond is liquid and the cash flows from the bond will not be an issue as the frequency of bond trading is good, also, the duration of the bond is not long means the bond is safeguarded from the long term market risk.

PLEASE SEE THE ATTACHED FILE.

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