Question

Part 1) Linda just sold all the shares of company A stock that she owned for $156/share. She purchased the stock one year ago for $150/share. Over the year, she received $1/share in dividend. Calculate the return on her investment.

Part 2) The interest rate on one-year Treasury-bond is 0.4%, the rate on two-year Treasury bond is 0.8%, the rate on three-year T-bond is 1.1%.

a. Compute the expected interest rate in the second year (year 2)

b. Compute the expected interest rate in the third year (year 3).

Part 3) The expected inflation rate for the next three years are estimated: 2.5% for 2020, 3.5% for 2021, and 4.2% for 2022. Calculate the inflation premiums (IP) for 1-year bond, for 2-year bond and 3- year bond.

Answer 1

Part 1)

The formula for return on investment is given as:

Substituting the given values, we get

which is equal to 4.67%

Part 2)

a. These type of questions can be solved by considering a no arbitrage condition. Essentially, the return an investor makes should be equal in the following 2 scenarios:

• Invests in one year treasury bond. After one year, the proceeds of this investment are again invested in a one year treasury bond.
• or, invests now in a 2 year treasury bond with annually compounding interest rate

Mathematically, this can be expressed as:

Substituting given values, we get

or 1.2%

b. Based on a similar logic we can also say that:

Substituting values we get

or 1.7%

Part 3)

Inflation premiums are simply the annualized equivalent of expected inflation rates. So, for 1 year bond, IP is equal to the inflation rate, 2.5%.

For 2 year bond we can say that:

or 2.9%

For 3 year bond

or 3.4%