4. 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) 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) What is the average 3M T-bill rate in the most recent 10-years, i.e. 2010/09 2012/08?

(iii) 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) 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.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) (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) 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) 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?

Datas can be found online