Question

1) A 7% Commonwealth government bond has three years to maturity. Given that the bond pays coupons semi-annually (i.e. twice a year) and a coupon payment has just been made, what is the present value (price) of the bond if the market interest rate is 9% and the face value of the bond is $100,000?

2) You have observed the returns for an investment in Telstra shares for the last five years. This shows returns of 23%, -17%, 8%, 22% and 3%. Calculate the average return, variance, and standard deviation of these shares.

3) You own a portfolio that is invested as follows: $11,600 in shares of Rendezvous hotel, $7,800 in shares of Crown Plaza, $14,900 in shares of Carlton & United Breweries, and $3,200 in shares of Domino’s Pizza . What is the portfolio weight of shares of Carlton & United Breweries?

4) One year ago, you bought a share for $36.48. You received a dividend of $1.62 per share last month and sold the share today for $40.18. What is the capital gains yield on this investment?

Answer 1

(a) Here, coupon rate is semi-annually so that coupon rate and market rate becomes half and time gets doubled.

Therefore,

Cash flow for an each year = $100000*(7/2)%

= $100000*3.5%

= $3500

Market rate = 9/2%

= 4.5%

Calculation of present value of bond :

(amount in $)

Time	Cash flow	PVIF 4.5%	Present Value
1	3500	[1/1.045]1 = 0.96	3360
2	3500	[1/1.045]2 = 0.92	3220
3	3500	[1/1.045]3 = 0.88	3080
4	3500	[1/1.045]4 = 0.84	2940
5	3500	[1/1.045]5 = 0.80	2800
6	103500	[1/1.045]6 = 0.77	79695
		Total	95095

Conclusion : Present value of 7% Commonwealth government bond after 3 years is $95095.

(b)

Returns(X)	dx = X -	(dx)2
23	23 - 7.80 = 15.20	(15.20)2 = 231.04
-17	-17 - 7.80 = -24.80	(-24.80)2 = 615.04
8	8 - 7.80 = 0.20	(0.20)2 = 0.04
22	22 - 7.80 = 14.20	(14.20)2 = 201.64
3	3 - 7.80 = -4.80	(-4.80)2 = 23.04
X = 39		(dx)2 = 1070.80

Average return () = X / Number of observation

= 39 / 5

= 7.80

Variance = (d_x)² / Number of observation

= 1070.80 / 5

= 214.16

Standard deviation =

=

= 14.63

(c) Total Investment = Sum of investment

= $11600 + $7800 + $14900 + $3200

= $37500

Portfolio weight of shares of Carlton & United Breweries = (Amount of shares in Carlton & United Breweries) / Total Investment

= $14900 / $37500

= 0.3973

Conclusion : Portfolio weight of shares of Carlton & United Breweries is 0.3973.

(d) Calulation of capital gain yield :

Capital gain yield =

=

=

= 14.58%

Hence, Capital gain yield on this investment is 14.58%.