A $100,000 bond has a term to maturity of one year. There are two coupon interest payments yet to be paid, one due in 6 months and the second to be paid along with the face value when the bond matures in one year. The coupon rate is 6% per annum, payable half-yearly, and the yield to maturity is 4% per annum, compounded half-yearly. The current price of the bond in $101,941.56.

(i)Calculate the duration of the bond.

(ii)Calculate the convexity of the bond.

b)A zero-coupon bond has one year to maturity and a face value of $100,000. The yield to maturity is 9% per annum, compounded half-yearly.

(i)Calculate the current price of the bond.

(ii)What is the duration of the bond?

c)Identify and briefly discuss 3 risks relating to Australian Government 10-year bonds.

1)[ 1 + 1 + 1 + 1= 4 marks]

a)Following an analysis, Leonard Bates has revealed the following utility preferences to different levels of wealth.

Wealth ($)Utility (Units)

100,00022

200,00032

300,00037

What do these figures imply about Leonard's risk preferences (or his willingness to

take risk)? Explain fully.

b)The share market is currently returning 12% per annum, while the risk-free asset is returning 4% per annum.Horace Hanley wishes to earn a return of 9%. What weight should Horace hold in the risk-free asset?

c)Assume Andrea Watson, an investor, has log utility. Andrea faces a choice between Investment X with a utility of 6.4000 and Investment Y, which will pay $400 in a bad state of the economy and $800 in a good state of the economy. [There are only two states.] What does the probability of the good state need to be for the investor to be indifferent between Investment X and Investment Y? [NOTE: Indifference arises when both investments have the same utility.]

d)Inestimating the covariance matrix, how many calculations are required for 15 assets under each of:

(i)The Markowitz approach; and

(ii)The Sharpe approach

respectively.

(a)With the aid of carefully labelled diagrams and equations, with all variables defined, describe carefully:

(i)The capital market line

(ii)The security market line.

Explain the advantage of the SML over the CML