security analysis & portfolio management set-2

8/6/2019 Security Analysis & Portfolio Management Set-2

1/4

Q 1. The following information is available on a bond:Face value : Rs100

Coupon rate: 12 percent payable annuallyYears to maturity: 6Current Market Price: Rs110YTM : 9 %What is the duration of the bond?

Ans.

Bond Duration is measure of bond price volatility, which captures both price andreinvestment risk and which is used to indicate how a bond will react in differentinterest rate environments.

The duration of a bond represents the length of time that elapses before the averagerupee of present value from the bond is received. Thus duration of a bond is theweighted average maturity or cash flow stream, where the weights are proportional tothe present balue of cash flows. Formally, it is defined as:

Duration = D = {PV (C1) x 1 + PV (C2) x 2+ ----- PV (Cn) x n } / Current Price of the bond

Where PV (Ci) is present values of cash flow at time

Annual Coupon payment = 12% x Rs. 100 = Rs. 12

At the end of 5 year, the principal of Rs. 100 will be returned to the investor.

Therefore cash flows in year 1-4= 12

Cash flow in year 5= Principal + Interest= Rs. 100 + Rs. 12= Rs. 112/-

Year

(t)

Annual

Cashflow

PVIF @

12%

Present Value

of AnnualCash flowPV(Ct)

Explanation Time Explanation

1 12 0.893 10.716 =12x0.893 10.716 =1x10.7162 12 0.797 09.564 =12x0.797 19.128 =2x09.5643 12 0.712 08.544 =12x0.712 25.632 =3x08.5444 12 0.636 07.632 =12x0.636 30.528 =4x07.6325 112 0.567 63.504 =12x0.567 317.52 =5x63.504

Total 99.96 403.524

Price of the bond= 99.96

The proportional change in the price of a bond:


2/4

(P/P) = - {D/ (1+ YTM)} x Y

Where Y = change in Yield, and YTM is the yield-to-maturity.The term D / (1+YTM) is also known as modified duration.

The modified duration for the bond in the question above= 4.03 / (1+12%) = 3.66years.

This implies that the price of the bond will decrease by 3.66 x 1% = 3.89% for a 1%increase in the interest rates.

Generally speaking, bond duration possesses the following properties: Bonds with higher coupon rates have shorter durations. Bonds with longer maturities have longer durations. Bonds with higher YTM lead to shorter duration

Durations of a bond with coupons is always less than its term to maturity because duration gives weight t the interim payments. A zero-coupon bondsduration is equal to its maturity.


3/4

2. Why did James Tobin call the portfolio T as super-efficient portfolio? Explain

Ans.

The characteristics of portfolios- expected return and standard deviation that combineinvesting in risk-free assets with investing in a risky assets plot on a straight lineconnecting the risky and risk- free point:

Let us combine the risk-free assets with risky assets on the efficient frontier. Being onthis line means that the investor is investing part of his money I the risk free asset andthe remaining money in the risky assets can be combined with any portfolio (say X or T) on the efficient frontier (EF). But all these combination would not be optimal. Whywould a rational investor choose any risky assets portfolio except the single one thatlies at the point of tangency between the efficient frontier and the straight lineextending from the risk free-assets? Only the tangency portfolio (portfolio T) would

be optimal for the investor. The tangent line (r-L) - which we will see in unit 10 iscalled the capital market line drawn to the efficient frontier passing thorough therisk free rate dominates all portfolios below it, including the efficient frontier. ThusPortfolio T is the optimal risky aversion. Tobin call the portfolio T as the superefficient portfolio.

Diagram from page No. 127


4/4

Q 3. What is Separation Theorem?

Ans.

Separation Theorem

If investors can borrow and lend, then everybody holds a combination of two portfolios:

1. A portfolio of Risk Assets (Tangency portfolio) that lies on the efficient frontier.

2. The risk free assets. The risk free asset and the tangency portfolio is the same for all investors if the live in a worlds of homogenous expectations, have the same one-

period horizon, and the same risk free rate and if information is freely and instantlyavailable to all.

Thus investor differs from each other (depending on their relative risk preferences)only by the proportions of the risk-free assets and tangency portfolio they choose tohold in their portfolio.

This portfolio construction is a two-step process. First, determine the risky portion of their portfolio the tangency portfolio on the efficient frontier that an investor wouldhold. The next step is to leverage (borrow at the risk free rate and invest further in thetangency portfolio) or de-leverage (sell part of the tangency portfolio and lend the

proceeds at the risk free rate) this portfolio to achieve whatever level of risk that theydesire.

We have seen that the composition of the tangency portfolio on the efficient frontier isthe same ofr all investors and is independent fo the investors appetite fro risk as it lieson the line drawn through the risk-free rate and tangent to the efficient frontier.

Therefore, the two decisions that the investors have to make:

1. choosing the composition of the risky portion of the investors portfolio, and

2. Deciding on the amount of leverage to use, are entirely independent of eachanother. One decision does not affect the other. This is called Tobinsseparation theorem . It states that the optimal combination of risky assets for an investor can be determined without any knowledge of the investors

preferences toward risks and return

security analysis & portfolio management set-2

Documents