Suppose the current yields to maturity on 3 month and 6 month T-Bills are 4.0 pe

Question

Suppose the current yields to maturity on 3 month and 6 month T-Bills are 4.0 percent and 5.0 percent, respectively (yields will need to be converted to 90-day returns).

(a) In perfectly efficient markets and risk-neutral pricing, what yield should you expect to find on a 3 month T-bill forward contract deliverable in 3 months?

(b) Show that for the forward yield calculated in (a) the 6 month returns on (i) a 6 month spot bill and (ii) 3 month spot and 3 month futures bills are the same.

(c) Explain what factors would lead to a rejection of (b).

NOTE: From the term structure of interest rates recall:

(1 + oy2)2 = (1 + oy1)(1 + 1F1)

where oy2 = the cash 6 month bill (two period) yield,

oy1 = the cash 3 month bill (one period) yield,

1F1 = the 3 month (one period) forward yield one period from now.

ALSO, in the futures market:

(1 + oy2)2 = (1 + oy1)(1 + 1y1f),

where 1y1f = the 3 month futures yield on futures contracts due in three months.

Explanation / Answer

a)   For perfectly efficient markets and risk-neutral pricing,

1+yield on a 3 month T-bill forward contract deliverable in 3 months*(90/360)=(1+0.05*(180/360))/(1+0.04*(90/360))

1+yield on a 3 month T-bill forward contract deliverable in 3 months*(1/4)=(1+0.025)/(1+0.01)

1+yield on a 3 month T-bill forward contract deliverable in 3 months*(1/4)=(1.025)/(1.01)=1.014851485

yield on a 3 month T-bill forward contract deliverable in 3 months*(1/4)=1.014851485-1=0.014851485

=>yield on a 3 month T-bill forward contract deliverable in 3 months=4*0.014851485=0.05940594=5.94%

b) the 6 month returns on a 6 month spot bill =(1+0.05*(180/360))-1=0.025

the 6 month returns on 3 month spot and 3 month futures bills (future yield due in three months=5.94%)

= (1+0.04*(90/360))(1+0.0594*(90/360))-1

=(1.01)*(1+0.0594*.25)-1

=0.025

Therefore the

the 6 month returns on (i) a 6 month spot bill and (ii) 3 month spot and 3 month futures bills are the same at 2.5%.

c)In case of risk averse investors who would demand risk premium on yield for the security they are holding due to interest rate risk and the illiquidity, the 3 month forward yield could be different from the one calculated.Therefore the demand for liquidity premium and the premium due to other risk factors could alter the 3 month forward yield from the one calculated. Therefore the investors demand for risk premium is what would cause the rejection of (b).

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