Question

An investor is presented with the following two alternative strategies: (1) Purchase a 5-year bond with an interest rate of 3.85% and hold it until maturity, or (2) purchase a 1-year bond with an interest rate of 4.00% and when it matures, purchase another 1-year bond with an expected rate of 1.75% and when that matures, purchase another 1-year bond with an interest rate of 6.50%. The investor can purchase a fourth 1-year bond with an interest rate of 1.75%. Finally, the investor can buy a fifth (and final) 1-year bond with an interest rate of 2.0%.

What is the expected annual return over 5 years for the first strategy?

What is the expected annual return over five years for the second strategy?

You would prefer the second strategy - true or false

Holding all else equal (i.e. investment strategy 1, as well as the rates on the first four bonds in strategy 2), what rate would you need to earn in the fifth year of the investment strategy 2 to be perfectly indifferent between the two strategies under the expectations process?

Answer 1

Answer A)

Assuming Bonds were purchased for 100 at Year 0

Strategy 1) Hold 5 year bond with annual interest of 3.85%

Year	Value (increase each year by 3.85%)
0	100
1	103.85
2	107.8482
3	112.0004
4	116.3124
5	120.7904

Return = Value at year 5 - Value at Year 0 = 120.7904 - 100 = 20.7904

Annual Return = (Total Return / Number of Years) / (Price at Year 0) * 100= 20.7904 / 5 = 4.1580 / 100 * 100 = 4.1580%

Answer B)

Strategy 2)

Year	Return	Value
0		100
1	4%	104
2	1.75%	105.82
3	6.50%	112.6983
4	1.75%	114.6705
5	2%	116.9639

Value at end of year = Value at beginning + (value at beginning * return%)

Total Return = Value at year 5 - Value at Year 0 = 116.9639 - 100 = 16.9639

Annual Return = (Total Return / Number of Years) / (Price at Year 0) * 100 = 16.9639 / 5 = 3.3927 /100 * 100 = 3.3927%

Answer C)

FALSE- We will not prefer second strategy. This is because Strategy 1 gives us a higher return.

Answer D)

In order to be perfectly indifferent between both strategies, we must earn a return of 5.33% in 5th year to make the return of strategy 2 equal to strategy 1. We use the goal seek function in excel to calculate this figure.

Steps to use the goal seek function:

(The above excel screenshot contains the values solved in earlier parts.)

1) Go to Data and Go to What if Analysis.

2) Select Goal Seek

3) Set Cell : (Select cell containing annual return of second strategy)

4) To Value : (Put in 4.158085)

5) By changing cell : (cell containing value of return of 5th year in strategy 2 i.e. cell containing 2% in above screenshot)

6) Press Ok.

We get the answer in the following screenshot: