Question

A dealer forecasts that the discount rate on a 60-day bill will be 5.10%. The current discount rate on a 90-day bill is 5.30%. What is the highest 30-day repo rate the dealer can afford to pay and still expect to break even? Explain your reasoning (and/or the setup to solve this question).

Answer 1

The maximum rate is 5.65%.

Explanation:

The break-even 30-day repo rate is the rate at which an investor can make zero profit by carrying the following described trading:

Initially raise 30-day repo at x rate; invest in 90-day bill at 5.30%;

As the 30-day repo is matured, raise fund from 60-day bill at 5.10% to repay the 30-day repo;

Then as the 60-day bill matures, use the proceed from 90-day bill to repay the amount.

In other word, we have the below calculation to illustrate the trading:

Amount repay to fund raising (through 30-day repo and 60-day bill) = Amount receipt from 90-day bill investment

[1 + x*30/365] x [ 1 + 5.1% *60/365 ] = 1 + 5.30% * 90/365

<=> 1 + x*30/365 = 1.004646 <=> x = 5.65%.