An investor's investment time horizon is two years. Spot rates for on-the-run annual-coupon government securities and swap spreads are shown as:

Maturity (years) 1 2 3 4

Government spot rate 0.5% 1.0% 1.25% 1.5%

Swap spread 0.25% 0.30% 0.5% 0.65%

The investor believes that interest rates will remain stable and the yield curve will not change its level or shape for the next two years. Swap spreads will also remain unchanged. The investor is considering 3 possible investments as follows. (Assume annual coupon payments throughout.)

(1) Employ a "riding the yield curve" strategy by buying a high quality four-year, zero-coupon corporate bond and then selling it after two years when yield would be lower. Assume the swap rate proxies for this corporate bond yield. What would be the annualized return over this horizon?

(2) Buy an off-the-run1.6% government bond with two years to maturity.  

(3) Buy a lower-quality, two-year 3% coupon corporate bond with a Z-spread of 200bpswith inside information that the bond is most unlikely to default in the next 3 years. What are the annualized returns of the 3 possible investments, and which will fetch the highest return?

Answer:

• The annual returns of all three investments are as follows :

Investment 1 = 3.01%

Investment 2 = 1%

Investment 3 = 2.993%

•  Investment 1 gives the highest return, so an investor should invest in investment 1.

Step-by-step explanation

• Calculation of annualized return for three investments:

             For Investment 1,

Riding the yield curve: It is a strategy that is used by investors when they expect the yield curve to remain upward sloping throughout the life of the bond. Under this strategy, the investor buys the bond and sells it before the maturity date to earn a capital gain.

In this case, the investor will buy a 4-year bond and sell it after 2 years to earn a capital gain.

The discounting rate to be used for this bond will be (government spot rate + swap spread) 

The calculation of capital gain and annualized return is shown below :

For Investment 2,

The calculation of annualized returns of 1.6% government bond with two years of maturity is shown below :

For Investment 3,

 Z-spread: It refers to the rate which is used to measure the present value of a bond's future cash flows by adding it to the government spot rate of each period.

The formula for calculating PV of bond while considering Z-spread is :

PV = (Coupon payment) / {1+(treasury spot rate1 + Z-spread)}^1+  (Coupon payment) / {1+(treasury spot rate2 + Z-spread)}^2 + ..........

The calculation of annualized returns of 3% corporate bond with two years of maturity with a Z-spread of 200 basis points(i.e 2%) is shown below :

• The return of all the three investments has been calculated above and it is clear that investment 1 provides the highest annualized returns and the investor would benefit the most by investing in investment 1.

Reference link :

https://www.investopedia.com/terms/z/zspread.asp

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