Question

Fixed Income: SHORT ANSWER QUESTION

1. You are an investment consultant working for a superannuation firm. One of the fixed-income portfolio managers wants to understand more about managing interest rate risk in the portfolio, and she is particularly interested in understanding the concept of duration. The portfolio currently contains option free bonds but the manager is considering adding bonds with embedded options into the portfolio. The manager is also considering purchasing a three-year 6% annual coupon paying bond. The one-year spot rate is 4%, the two-year spot rate is 3%, and the three-year spot rate is 4%. What is the value of the option free bond that is being considered for purchase? State all formula and working used.

2. The relationship between bond prices and yields is very important to fixed-income investors. Explain the characteristics of a bond that affect its price volatility.            

3.Calculate the convexity adjustment for a bond if the initial price is $104.45, price if yields increase by one percent is $100 and price if yields decrease by one percent is $109.16. Show all formulas used.   

Answer 1

1). Value of the option free bond = sum of cash flows discounted at the respective spot rates

Annual coupon = coupon rate*par value = 6%*1,000 = 60 (assuming a par value of 1,000 since it is not mentioned in the question)

Value = coupon 1/(1+ one year spot rate) + coupon 2/(1 + two year coupon rate)^2 + (coupon 3 + par value)/(1 + three year coupon rate)^3

= 60/(1+4%) + 60/(1+3%)^2 + (60 + 1,000)/(1+4%)^3 = 1,056.58

(Note: If par value is taken to be 100 then value of the bond will be 105.658 or 105.66)

2). Price volatility of an option free bond is mainly affected by two factors - coupon rate and term to maturity of the bond. A bond with a longer term to maturity will have higher price volatility. Also, higher the coupon rate, lower will be the price volatility.

3). Approximate convexity is measured by [P+ + P- - 2P0]/(P0*change in yield^2)

where P+ = price when yield increases by 1%; P- = price when yield decreased by 1%; P0 = initial price; change in yield = 0.01

Approximate convexity = (100 + 109.16 - (2*104.45))/(104.45*0.01^2) = 24.89