Consider the following term and YTM of 5 hypothetical Treasury securities with a par value of 100 Ksh.

Term Coupon rate YTM price

0.5 0 0.080 96.15

1 0.0 0.083 92.19

1.5 0.085 0.089 99.45

2 0.09 0.092 99.64

2.5 0.11 0.94 103.49

Calculate

(1) Theoretical spot rate for :

1.5 year coupon bond

2 year coupon bond

2.5 year coupon bond

(2) Consider a 2.5 year, 9% coupon bond with a par value of 100 Ksh. What is its theoretical value given the previously calculated theoretical spot rates?

(3) Using the previously calculated spot rates calculate:

i)The 6-months forward rate 6 months from now

ii)The 1yr forward rate 1.5 years from now

Question B

Assuming annual payments calculate Macaulay duration of a 4%, 10-year, Ksh 1000 par bond, if the YTM is 8 percent:

QUESTION C

i)Calculate Duration (D) of five-year 10% bond with a face value of $1,000 and a current market price of $1,123.02. The current yield to maturity is 7%. Assume annual coupon payments

ii)Calculate Duration (D) of five-year 10% bond with a face value of $1,000.The current yield to maturity is 8%.Assume annual coupon payments

QUESTION D

Calculate the convexity of a 3 year, Ksh 1000par 12% coupon bond with a yield to maturity of 9%.

QUESTION E

The price of 5% coupon bond with a 1000 Ksh principal and 4 years to maturity is 870.47. If interest rates change by 50 basis points from 9.0% to 9.5% the price would be 855.80 and 885.35 if the interest rates change from 9.0 to 8.5% (50 basis price decrease). What is the duration of the bond?

QUESTION F

Edison Inc. issued warrants for the period April 2003 to December 2007. The details of the warrants are as follows:

Amount issued: 1,094,831,000

Number of outstanding shares: 4,079,070,000

Current price of the warrant: $0.390

Life to final date: 4.46 years

Risk-free rate: 3.05%

Equity price: $1.134

Strike price: $1

Volatility (annualized standard deviation): 43.72%

What is the value of the warrant?

QUESTION G

Vilmorin Inc issued a convertible Bond Issue worth $150m in June 2008 with the following details:

Issue price: $155.96

Face value: $155.96

Issue date: 6 June 2008

Maturity: 1 July 2015

Interest rate: 4.50% ($7.0182 coupon)

Market price: $155.96

Conversion ratio: 1 share for 1 bond

Conversion period: From 6 June 2008 to 22 June 2015

Vilmorin share price at the time of issue: $129.97

Calculate:

i)The conversion price

ii)The conversion premium

QUESTION F

KBC company preferred stock has a par value of KSh100and a Ksh 9 dividend rate. You require an 11% rate of return on this stock.

i)What is the maximum price you would pay for it

ii)Would you buy it at Ksh 96?

QUESTION G

a) Assume that the economy has 4 equally likely states of outcomes Depression Recession Normal and Boom. This means that each of these states of outcomes have a 0.25 chance of occurrence. Kenya Airways expect that the following returns would be made in the states of Outcomes respectively -20 %10% 30% and 50%.

The expected returns ( ) for the Kenya Airways will be:

b) If the weights for the possibilities (states of outcomes) were to change to 0.1, 0.2, 0.6 and 0.1 respectively for Kenya Airways what be the expected return?

c)Using data from (a) of KQ, calculate its standard deviation

d) Similarly consider Safaricom operating the in same possible states of outcomes but with the following expected return respectively, 5%, 20%, -12% and 9%. What is the standard deviation?

e) Work out the spread for 95.4 and 99.9% confidence level for KQ & SF

QUESTION H

consider the following example stocks assuming you have already computed betas:

Stock

Beta

A

0.80

B

1.00

C

1.50

D

1.30

E

-0.50

Assume that we expect the economy's RFR to be 5 percent (0.05) and the return on the market portfolio (R_M) to be 10 percent (0.10). This implies a market risk premium of 5 percent (0.05). With these inputs, the SML equation would yield the following expected (required) rates of return for these five stocks:

QUESTION I

1.Assume the risk free rate is 10% and the expected return on the market portfolio is 15%. Market analysts return expectations for four stocks are listed below:

Stock

Expected return

Beta

Safaricom

17.0

1.3

Rift valleyRailways

14.5

0.8

Lake Victoria Fish

15.5

1.1

Oserian Flowers

18.0

1.7

(a) If the analysts' expectations are correct, which stocks (if any) are overvalued and which (if any) are undervalued?

(b) If the risk free rate were to suddenly rise to 12% and the expected return on the market portfolio to 16%. Which stocks (if any) would be overvalued and which (if any) are undervalued? (Assume the market analysts' return expectations remain the same for the four stocks)

2.Suppose T bills have an 8% expected return, and the expected return on market portfolio is 13%, and the beta of Kenya Airways is 1.3.

i)What is the required rate of return for KQ will be

ii)If beta for KQ = 1.0

iii)If beta for KQ = 0.7

An analyst wishes to study how expenditure on travel by an individual varies with their gender and employment status. They collect cross-sectional data for these variables and the data is as follows:

Travel expenditure in dollars

Gender

Employment Status

40

Male

Employed

31

Female

Unemployed

18

Male

Unemployed

19

Male

Unemployed

47

Male

Employed

27

Female

Unemployed

26

Female

Unemployed

17

Male

Unemployed

43

Male

Employed

49

Male

Employed

15

Male

Unemployed

25

Female

Unemployed

29

Female

Unemployed

20

Male

Unemployed

41

male

Employed

Required:

(i)Taking gender as D1i = 1 if individual is female, but 0 otherwise; and employment status as D2i = 1 if employed, but 0 otherwise; regress travel expenditure on gender and employment status

(ii)Interpret the results of the estimated regression model

(iii)What expenditure value will a male unemployed person make?

(iv)Calculate R² and adjusted R²

(v)Test for the overall significance of the model

(vi)Derive the variance-covariance matrix, and test for the statistical significance for each parameter in the model

Consider the following data which shows the amount of time in hours people spend watching the television as a function of their age and gender:

Hours watching TV

Gender

Age of individual

0

Male

41

180

Male

19

360

Female

54

900

Male

22

0

Male

48

360

Female

52

3600

Female

24

630

Male

60

1440

Female

28

0

Male

58

360

Female

35

4680

Female

67

630

Female

30

1440

Female

21

90

Male

32

360

Male

33

5760

Female

39

720

Female

56

2160

Female

31

90

male

57

In order to regress hours on gender and age, we can define the model as follows:

Y_i = b₀ + b₁D + b₂X + u_i

Where: Y_i = the number of hours individuals spend watching TV.

D = gender, such that D = 1 if male, 0 otherwise

X = age of individual in years.

Required:

(a)Regress hours against gender and age of individual and interpret the results of the model

(b)Compute R-squared and adjusted R-squared

(c)Derive the variance-covariance matrix and use it to obtain the standard errors of the regression coefficients

(d)Test the statistical significance of:

(i)The regression parameters

(ii)The regression model