Price will the bond sell

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A Treasury bond with £100 maturity value has a £6 annual coupon and 4 years left to maturity.
i. What price will the bond sell for assuming that the 4-year yield to maturity in the market is 7%? (Show your calculations)
ii. What would be your answer to part (i) if the 4-year yield to maturity in the market is 9%? (Show your calculations)
iii. What does your answer to parts (i) and (ii) tell you about the relationship of bond prices, term to maturity and changes in bond yields? (2 marks)
 
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The Macaulay Duration

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i. Calculate the Macaulay Duration for a £7 annual coupon bond with an original face value of £100.. The bond has 4 years left to maturity and a current yield to maturity of 8%. (Show your calculations)
ii. What is the modified Duration of the bond?
iii. If 4-year yields to maturity were to suddenly increase from 8% to 8.5% and the bond in problem (i) was selling for £96.69 at 8% yield, what would you expect the bond price to be after the yield increases to 8.5%?
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Returns on security

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You are given the following data about the expected one year returns on security A, RA and security B, RB. along with the standard deviations of returns on asset A, σA and the standard deviations of returns on asset B, σB. Complete the following table for standard deviations of the portfolio for the two values of the correlation coefficient of returns on securities A and B (ρAB) and the differing weights attached to the two securities wA and wB. (Show you workings in full)
RA = 15%, σA = 60%
RB = 10%, σB = 30%
wA wB ρAB=0.5 ρAB=0 Return
0.8 0.2 ? ? ?
0.2 0.8 ? ? ?
 
 
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Investments in securities

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You have following investments in securities A, B and C.
Security Amount Invested Beta Expected one year return
A £10,000 1.15 14%
B £10,000 1.90 20%
C £5,000 1.72 18%
The current risk-free rate of interest is 4% and you have heard that analysts are expecting a 12% return on the market portfolio over the next year. Based on your expectations for the 1-year returns of each of the securities is your portfolio under-priced, overpriced or correctly priced?
 
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