QUESTION $1$

$[25$ Marks$]$

$($a$)$ Calculate and explain the Bond Macaulay Duration for a $3-$year bond, carrying $6$ percent coupon and a market yield of $10$ percent.

$(10$ Marks$)$

$($b$)$ What is the Bond's Modified Macaulay Duration in $($a$)$ and what is its interpretation?

$(7$ Marks$)$

$($c$)$ Discuss any four factors that determine a Bond's Duration.

$(8$ Marks$)$

QUESTION $2$

$[25$ Marks$]$

Consider the following expected daily returns $($in terms of South African Rand currency$),$ standard deviations and correlations:

$\backslash$table$[[$Botswana$,$ South Africa and Namibia Bond Returns,$],[$Rand Daily Returns in $\%,],[,$Botswana Bonds,South Africa Bonds,Namibia Bonds$],[$Expected Returns,$0\mathrm{.}02,0\mathrm{.}015,0\mathrm{.}07],[$Standard Deviation,$0\mathrm{.}4,0\mathrm{.}6,0\mathrm{.}7]]$

$\backslash$table$[[$Correlation Matrix,Botswana Bonds,South Africa Bonds,Namibia Bonds$],[,1,0\mathrm{.}09,0\mathrm{.}1,,,,],[$Botswana Bonds,$1,1,0\mathrm{.}7,,,,],[$South Africa Bonds,$0\mathrm{.}09,0\mathrm{.}7,1,,,,],[$Namibia Bonds,$0\mathrm{.}1,,,,]]$

a$)$ Create a covariance matrix for the daily returns on the three bonds listed above

$[15$ marks$]$

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b$)$ Compute the expected return and variance of return a portfolio $70\%$ invested in Botswana Bonds, $20\%$ in South Africa Bonds, $10\%$ in Namibia Bonds

$[5$ marks$]$

c$)$ Compute the standard deviation of return for the portfolio in b$)$ above

$[5$ mark$]$