Question

A $5,000 payment is owed from Abby to Ben two years from now. Abby wants to set up an investment fund to meet this obligation, but the only investments she has available are a money market fund (currently earning 8%, but the rate changes daily), and a five-year zero-coupon bond earning 8%. Use an immunization framework to determine the amount of money Abby should invest now in each of the two investment vehicles. Assume an effective annual interest rate of 8% for present value calculations.

Answer 1

Here we will use immunization method for asset liability management.as per this method liabilities is said to be immunised if duration of liabilities gets equal to duration of assets

i.e. weighted Average Duration of Assets(Da) = duration of total liabilities(DL)

DA = W1*D1+W2*D2

where W1 = weight for asset1 i.e. money market fund

D1= Duration of asset 1 since we are not given what type of asset class in which this fund falls so let us assume that it is a perpetual fund so its duration is given by

duration of an asst having perpetual life = (1+i)/i =1.08/.08= 13.5year

W2= weight of asset 2 i.e. zero coupon bond, W2 = 1-W1

D2 = duration of asset 2 = maturity of ZCB = 5 years

DL = duration of liability.Since liability is a single cashflow = time of liability = 2 years

2=W1*13.5 +(1-W1)*5

2=13.5W1 +5 - 5W1

8.5W1 =3

W1=3/8.5= .3529

W2=1-.3529 =.6471

amount to be invested in Asset 2 i.e. ZCB = F*W2/(1.08)^5

F*W2 = Face value purchased = 5000*.6471 =3235.5$

investment in ZCB = 3235.5/1.08^5 = 2202.03$

investment in perpetual money market fund= .3529*5000*.08/.08= 1764.5$