Question

3 (AAR and GAR): The price of a security is $100 at time 0, $50 at time 1, and $100 at time 2. What’s the AAR and GAR?

4 (FETY): A tax-exempt bond has a yield of 6%, exempt from both federal taxes (30%) and state taxes (10%). What’s the FETY of a corporate bond on which both federal and state taxes apply?

5 (yields): A 90-day T-bills pays $10,000 at maturity, the current price is $9875. What’s the bank discount rate? The bond equivalent yield? Effective annual yield?

7. (CAPM): What’s the expected return for a security with beta=0.8? The market risk-premium is 4% and risk-free rate is 0.5%. Now the actual return of the security is 4%, is it a buy signal or a sell signal?

Answer 1

3)	The periodic returns of the security are calculated below:
	Time	Value	Return for the period
	0	100
	1	50	-50.00%
	2	100	100.00%
	AAR = (-50+100)/2 = 25%
	GAR = ((1-0.5)*(1+1))^(1/2)-1 =		0.00%
4)	FETY of a corporate bond = 0.06/(1-40%) =			10.00%
5)	Bank discount rate = (10000-9875)/10000 =			1.25%
	Discount rate per annum = 1.25%*90/360 =			5.00%
	Bond equivalent yield = (125/9875)*365/90 =			5.13%
	Effective annual yield = (1+125/9875)^(365/90)-1 =			5.23%
7)	Expected return per CAPM = Risk free rate+Beta*Market risk premium
	= 0.5%+0.8*4% =		3.70%
	If the actual return of the security is 4%, it means that the
	security is undervalued. It is a buy signal.