T = 0. You have $20,000 that you are willing to investing for 3 years. You are c
ID: 2623136 • Letter: T
Question
T = 0. You have $20,000 that you are willing to investing for 3 years. You are considering three different potential strategies. They are:
Strategy 1: Invest in a 3 year zero with a current (i.e., t = 0) yield to maturity of 3 percent.
Strategy 2: Invest in a 1-year zero with a current (i.e., t = 0) yield to maturity of 1 percent; then next year (when the current 1-year zero matures) invest in a two year zero at whatever the yield to maturity on two-year zeros are then (at t = 1).
Strategy 3: Invest in a 5 year zero with a current yield to maturity of 3.5 percent and sell these bonds in three years (at t = 3).
If the yield curves at t = 1 and t = 3 are as shown below, which of these three strategies will turn out the best? That is, after 3 years, which strategy will generate the largest amount of money?
t = 1 Yield Curve: t = 3 Yield Curve: .
Time to maturity YTM Time to Maturity YTM
(in years) (in years)
1 .02 1 .02
2 .022 2 .025
3 .025 3 .035
4 .030 4 .045
Explanation / Answer
We will calculate the returns from each strategy.
Strategy 1:
As this is a 3 year zero coupon bond with Yield to Maturity (YTM) of 3%, the realized annual return is 3% after 3 years.
Strategy 2:
Investing in 1 year zero coupon bond gives us 1% for the first year.
After year 1, the YTM for 2 year zero coupon yield can be seen from the given table - this is 0.022 or 2.2%.
So annual return for the 3 years together = ( (1+1%) * (1+2.2%)^2 ) ^ (1/3) - 1 = 1.80%
Strategy 3:
After year 3, the YTM for 2 year zero coupon yield can be seen from the given table - this is 0.025 or 2.5%.
Let annual return for the first 3 years be X%.
So (1+X)^3 * (1+2.5%)^2 = (1+3.5%)^5
Solving, we get X = 4.17%
Comparing the 3 strategies, we see annual returns for strategy 1 = 3%, strategy 2 = 1.80%, strategy 3 = 4.17%.
As strategy 3 has the highest annual return among the 3, we should choose strategy 3 as the best option.
Hope this helped ! Let me know in case of any queries.
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