Question

You want to make a one-year investment in a fixed-income security. You have two investment choices: a Treasury security and a Treasury inflation-protected security (TIPS). The nominal interest rate for the Treasury security is 4% and TIPS promises 1% real interest rate. You use scenario analysis to compare two securities. There are two possible scenarios with equal probabilities: High inflation and low inflation. The inflation rate will be 0% in the low state and 6.1% in the high state. (Do not use % approximation by adding or subtracting)

(a) Compute nominal and real realized returns for each asset with respect to each inflation scenario, and calculate expected return of each asset. (Round to the nearest tenth)

Nominal Returns Before Taxes

	Low Inflation	High Inflation	Expected Return
Treasury Security
TIPS

Real Returns Before Taxes

	Low Inflation	High Inflation	Expected Return
Treasury Security
TIPS

b) According to (a), which security will investors choose?

c) Now suppose the investor is subject to tax with marginal tax rate 40%. Compute nominal and real realized returns for each asset with respect to each inflation scenario, and calculate expected return of each asset. (Round to the nearest tenth)

Nominal Returns Before Taxes

	Low Inflation	High Inflation	Expected Return
Treasury Security
TIPS

Real Returns After Taxes

	Low Inflation	High Inflation	Expected Return
Treasury Security
TIPS

(d) What security would the investor choose if the investor has to pay tax with marginal tax rate 40%?

e) Explain why expected return and risk of TIPS changed after taxes.

Answer 1

a.Nominal Returns Before Taxes
	Low Inflation	High Inflation		Expected Return
Treasury Security	4%	4%*(1.061)=	4.244%	(4%*50%)+(4.244*50%)=	2.142%
TIPS	1%	((1.01)*(1.061))-1=	7.161%	(50%*1%)+(50%*7.161%)=	4%
Real Returns Before Taxes
	Low Inflation	High Inflation		Expected Return
Treasury Security	4%	(1.04/1.061)-1=	-1.979%	(50%*4%)+(50%*-1.979%)=	1.0105%
TIPS	1%		1%	(50%*1%)+(50%*1%)	1%
b) According to (a), investors will choose TIPS as the expected returns are more in Nominal terms & also negligibly low , in real terms --compared to the treasury security.

c..Nominal Returns after Taxes
	Low Inflation		High Inflation		Exp.Return
Treasury Security	4%*(1-40%)=	2.40%	4%*(1.061)*(1-40%)=	2.5464%	2.4732%
TIPS	1%*(1-40%)=	0.60%	(((1.01)*(1.061))-1)*(1-40%)=	4.2966%	2.45%
Real Returns After Taxes
	Low Inflation		High Inflation		Exp.Return
Treasury Security	4%*(1-40%)=	2.40%	((1.04/1.061)-1)*(1-40%)=	-0.011876	0.6062%
TIPS	1%*(1-40%)=	0.60%	1%*(1-40%)=	0.60%	0.60%
d..According to (c), investors will choose Treasury security as it's returns are > TIPS both in Nominal & Real terms

e. Expected return on TIPS decreases due to taxes.
Risk is that , if there is no inflation,then holding TIPS may not be fruitful, because of low-interest payments.
If there is inflation, tax bill increases, as coupon interests are based on the revised Principal, keeping in line with the inflation rate as per the Consumer Price Index.