Question

You are managing an investment portfolio X on behalf of your clients. Assume the assets within portfolio X belong to three asset classes: stocks, fixed income and cash, with weights 60%, 9% and 31%. Suppose the benchmark index weights had been set at 65% equity, 18 % bonds and 17% money market. Question 2 (8 marks) The return of the benchmark index and the managed portfolio X for each asset class for last year were as follows Benchmark Index Portfolio X 8.28% 6.50% Stocks 1.45% 0.68% 2.89% Bonds 0.30% Money Market a. Calculate the excess return of portfolio X [3 marks] b. Let's focus on the bond asset classes among the portfolio X You have a one-year, $100,000 bond carries a coupon rate of 10 % . The bond will make the payment of accrued nterest and one-half of the principal at the end of six months. The remaining principal and accrued interest are due at the end of the year. If the required yield is 20% annually, what is the duration of the bond? [Please keep three decimals]. [5 marks] Page 5 of 6 ibris, a ProQuest Compay, 2019 Pottelio Manage dent, telehuntes, Sptly sades AutoReco. MACR OFEXAM NO. Documen OV

Answer 1

a. Excess return of portfolio X=

Weighted returns of Portfolio X -Weighted return of Benchmark Index assets

ie.((8.28%*60%)+(2.89%*9%)+(0.30%*31%))-((6.50%*65%)+(1.45%*18%)+(0.68%*17%))=

0.72%

b..
Semi-annual periods	Cash flow	PV of $ 1 at 10%(semi-annualYTM)	PV of cash flows	Semi-annual periods*Cash flows	PV of Col.5
1=n	2	3=1/1.1^n	4=2*3%	5=1*2	6=3*5
1	55000	0.90909	50000	55000	50000
2	52500	0.82645	43388.43	105000	86776.86
Total			93388.43		136776.86
Note: 50000+(100000*10%/2)=55000 &
50000+(50000*10%/2)= 52500
Macaulay Duration of the bond= Sum of PV of period weighted cashflows/Current bond value
ie. 136776.86/93888.43=
1.457
Modified duration= Macaulay duration/(1+Semi-annual Yield)
1.457/(1+0.1)=
1.325