When we use the CAPM model to estimate the cost of capital for a 10-year project, ideally we would like to find the average expected short-term rates (yields) of risk-free securities (e.g. 1M or 3M T-bills) for the next 10 years and use it as the proxy for the risk-free rate in the CAPM model. However, in practice, the expected short-term rates for the next 10 years are not readily available. One way is to look at historical 3M T-bill rates, and use some sort of historical average as the estimate for the average expected short-term risk-free rates for the next 10 years.

(i) (5 pt) Find the historical 3M T-bill rates (monthly frequency) from the past 40 years (1980/09-2020/08) from the Internet, and plot the historical 3M T-bill rates against time (horizontal axis: time; vertical axis: 3M T-bill rate)

(ii) (2 pt) What is the average 3M T-bill rate in the most recent 10-years, i.e. 2010/09 2020/08?

(iii) (5 pt) Calculate the averages of 3M T-bill rates from the 10, 20, and 30 years prior to 2010 (i.e. 2000-2009, 1990-2009, 1980-2009 respectively). Do these historical averages prior to 2010 provide good estimates for the actual (realized) 3M T-bill rates in the subsequent 10 years (2010-2020) as you calculated in (ii)?

(iv) (4 pt) Based on your answers in (ii) & (iii) above, discuss the issues we may encounter when we use historical 3M T-bill rates to estimate expected future 3M T-bill rates.

5. (8 pt) Given the issues discussed in Question 4 above, some people look at the current yield (rate) of 10-year treasury notes instead and use it as the point estimate of current average expected short-term risk-free rates for the next 10 years.

(i) (3 pt) (a) What is the current yield of 10-year treasury notes? (b) How about current 3M T-bill rate? (c) Which rate is higher?

(ii) (3 pt) Are 10-year treasury notes really risk-free? Compared to 3M T-bills, what are the potential risks associated with longer dated treasury securities?

(iii) (2 pt) Given the issues discussed in (ii) above, what adjustments should we make when we use the 10-year treasure rate (yield) as the starting point of risk-free rate estimate? Or should we use approach and why?