question check – please check mock exam answer

Question

Hi,

On a mock exam question, I was asked to determine the cost of equity (riskfree rate plus market premium times beta). I got the question wrong because I used 3 month t bill rate instead of 10 year treasury rate.

Isn't the 3 month t bill rate usually considered the risk free rate?

Thank you in advance! Just want to make sure I understand how to answer for this coming Saturday!

CFA_anon · Answer

Sorry for the late comment, I hope the exam went well for you! The choice of rate is usually dependent on the time horizon you are using. Technically, you should be using zero-coupon treasury bonds (STRIPS in the US) for the rate to REALLY make it riskless.The reason?There are two basic conditions that have to be met for a risk-free security.-No default risk-No reinvestment risk (in order to have an actual return equal to its expected return)One way is taking the yield curve and solving for the zero-coupon rates at each tenor, if you are in the US, US Treasury STRIPS are traded, so easily done. To illustrate this point, assume that you are
trying to estimate the expected return over a five-year period, and that you want a
risk free rate. A six-month treasury bill rate, while default free, will not be risk
free, because there is the reinvestment risk of not knowing what the treasury bill
rate will be in six months. Even a 5-year treasury bond is not risk free, since the
coupons on the bond will be reinvested at rates that cannot be predicted today.
The risk free rate for a five-year time horizon has to be the expected return on a
default-free (government) five-year zero coupon bond.
In summary, an investment can be riskfree only if it is issued by an entity with no default
risk, and the specific instrument used to derive the riskfree rate will vary depending upon
the period over which you want the return to be guaranteed.
Although, in the exam, they probably just want you to use the yield on the 10-year for simplicity sake.