Question

1. Suppose the investor finds a tax free security that pays 6%. The investor's tax rate on taxable securities is 30%. Find the tax equivalent yield. 2. Find the yield on a 30 day debt security if Rn-2%, DP -3%, LP 2% and TA-. 1 %. 3. Assume tl,--6%,-3%, ti,-2%. Find the one and two year forward rates for a one year security.

Answer 1

1.

Tax equivalent yield is used to compare the yields of tax exempt securities to that of taxable securities. It is given by the formula:

$Tax\:equivalent\:yield=\frac{yield\:on \:tax\: free\: security}{1-tax\:rate}$

$Tax\:equivalent\:yield=\frac{0.06}{1-0.3}$

= 8.57%

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2.

The formula to calculate yield of an n day security is:

$Y_{n}=R_{f,n}+DP+LP+TA$

where,

• $Y_{n}$ is the yield to be calculated
• $R_{f,n}$ is the risk free yield
• DP is the default premium
• LP is the liquidity premium
• TA is adjustments due to difference in tax status

Yield = 2% + 3% + 2% + 1% = 8%

3.

Forward rates are interest rates that are decided now, for a transaction that is going to happen sometime in the future. The figure below shows the spot rates rates for periods 1, 2 and 3 respectively as given in the question. The one year forward rate is then denoted by $f_{_{1}}$. The rate is fixed today between investor and borrower i.e. at time period 0. The actual transaction happens at period 1 and the transaction concludes at period 2.

Now to calculate one year forward rate $f_{_{1}}$ we can use the following equation:

$(1+0.02)(1+f_{1})=(1+0.03)^{2}$

this equation simply means that the return an investor would get by holding a 1 year security and a 1 year forward security is equal to him holding a 2 year security i.e. there is no opportunity for arbitrage.

On solving we get

$f_{1}$=4%

Similarly we can write an equation for 2 year forward rate as:

$(1+0.03)^{2}(1+f_{2})=(1+0.06)^{^{3}}$

On solving, we get

$f_{2}$=12.3%