Unformatted text preview: interest rate risks: Income risk and Price risk.
Income risk relates to uncertainty in reinvestment income and arises when investors hold a bond for a period
that is beyond the payment of one coupon interest.
Price risk relates to the uncertainty in selling price and arises when investors hold a bond for a period that falls
short of its maturity.
Income and Price risk offset one another: Interest Rate , Coupon Reinvestment Rate , Coupons , Price Interest Rate , Coupon Reinvestment Rate , Coupons , Price However, income and price risk often do not offset each other completely and the investor earns different
returns from ones they expect. Due to the offsetting nature of the 2 types of interest rate risk, we should be
able to find an optimal holding period for those who would like to get rid of interest rate risks. When these
risks are negated, investors earn the same return as expected. This optimal holding period is given by the
bond’s Macaulay Duration. M ACAULAY DURATION
The Macaulay Duration (MacDur) of a bond is defined as the weighted average time for an investor to recover
the cost of a bond investment.
C ALCULATING MACDUR t
PV CFt CFt 1 y D wt t t t
t 1 PV CFt t 1 T T t The weights, w1, w2 and wt-1 correspond to the proportion of initial cost recovered from the present
value of the 1st, 2nd and second last coupon interest
Wt corresponds to the proportion of initial outlay recovered from the present value of the last coupon
interest and face value.
T1, t2 and tt-1 correspond to the time when the last coupon interest and face value is received.
tn corresponds to the time when the last coupon interest payment and face value is received.
As MacDur should be expressed per annum, the ending D should be divided by the no. of coupon
payments per year. 9 Cheryl Mew FINS2624 – Portfolio Management Semester 1, 2011 C UM AND EX-INTEREST BONDS
To Calculate the Cum and Ex-Interest Bonds’ MacDur, the same formula is to be applied. However, in this case,
the t will be a decimal. E.g. for...
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