Immunization, Financial Management

Assignment Help:

In 1952, to provide equilibrium between assets and liabilities of insurance companies, Frank Redington, an English actuary, proposed interest rate immunization technique. Later in 1971, the same concept was extended to bond portfolios by Fisher and Weil.

A variation in interest rate will result in two opposite effects. An increase in the interest rates will decrease the value of bond portfolio, but leads to higher return on the coupons reinvestment. The basic mechanism underlying the concept of portfolio immunization is 'portfolio structure'. A portfolio structure balances the change in the value of the portfolio at the end of the investment horizon with the returns from the reinvestment of portfolio coupons payments. Thus, immunization can be defined as a process of offsetting price risk and reinvestment risk.

For example, let us assume that an investor is holding a bond with 5 years maturity and 8 percent coupon rate at a price (quoted) of Rs.108.42. The yield of bond is 6 percent. The investor wants to know the final wealth for different time horizons in case some unexpected variation occurs in the market yield today (the market yield would remain stable after this).

The results for 1 to 5 years time-horizons, and 4% to 8% final market yield (i.e., a variation of ±2%) can be seen in the following table:

Table 1: The Effect of a Yield Variation on Terminal Wealth

Time Horizon

New Market Yield

4%

5%

6%

7%

8%

 

1 year

122.52

118.64

114.93

111.39

108.00

2 years

127.42

124.57

121.83

119.18

116.64

3 years

132.52

130.80

129.14

127.53

125.97

4 years

137.82

137.34

136.88

136.45

136.05

5 years

143.33

144.21

145.10

146.01

146.93

The above results are shown in the form of graph in the following figure:

Figure 2: The Effect of a Yield Variation on Terminal Wealth

244_effect of yield variation.png

The final wealth differs slightly from the status quo assumption (in the absence of variation we would be on the curve H0.06). On short time-horizon, the effect on the bond price is higher when compared to the effect on the reinvestment of the coupons and the investor wishes to avoid an increase in interest rate. In the case of longer time-horizons, the reinvestment of coupons grabs a higher part of the final wealth and the investor tries to avoid decrease in interest rate.

An interesting point to be noted here is, there appears to be a time horizon
(4.34 years) for which the final wealth will be the same, whatever the initial interest rate variation may be. If such a time-horizon is selected, it will result in 6% yield and a final wealth of:

W=108.42(1.06)434=139.64

Now, the portfolio is said to be immunized against interest rate variations. It can be shown theoretically that time-horizon is the duration of the bond that is considered. Thus, an investor can avoid interest rates variations if he selects a portfolio with duration equal to its time horizon.

The major problem here is, time-horizon is not a variable, but it is a given value. That means, the investor will not modify the time-horizon to immunize the portfolio, but he will be given a time-horizon for which he has to immunize the portfolio. Now, let us see how to select a set of securities whose stream of cash flows has duration equal to the time horizon of the investor.

It might sound simple to do so, by just creating a portfolio with duration equal to the time horizon of the investor (because portfolio duration is the weighted average of the durations of the individual issues):

         Duration = Time Horizon (= TH)

However, the above condition alone is not sufficient for our purpose:

  • As discussed earlier, duration does not change continuously with the lapse of time, but the investor's time horizon declines continuously with the lapse of time. So, in order to ensure that duration and time-horizon remain equal, a portfolio has to be balanced whenever there is a liability payment due.

  • Whenever there is an interest rate modification, an immunized portfolio is not immunized further, as its duration gets modified. For this reason, every portfolio should be theoretically rebalanced after each change in interest rates.

  • Lastly, the coupon payment modifies the portfolio duration in a non-linear form. Further, their reinvestment may also affect the immunization equilibrium.

Because of all the above reasons, immunization has to be a dynamic process. To serve this purpose, the portfolio to be immunized should be written as:

Durationt=Time horizont (for all t)

The portfolio must be frequently rebalanced to satisfy this condition.       


Related Discussions:- Immunization

Evaluate financial report and analysis, Project Specifications Complete...

Project Specifications Complete an individual Financial Report and Analysis. You will select a company that you would like to analyze based on the parameters provided by the

What are the characteristics of an efficient market?, What are the characte...

What are the characteristics of an efficient market? The term market efficiency denotes to the ease, speed, and cost of trading securities. In an efficient market the securitie

Cash flows from mortgage- backed security, It is a well known fact th...

It is a well known fact that the value of a financial claim reflects the present value of the cash flows produced by the financial claim. While valuing an MBS an

Yield to worst, Now we can calculate the yield for each possible call...

Now we can calculate the yield for each possible call or put date. In addition, we can also calculate the yield to maturity. The lowest yield of all these possibl

How does accounts receivable factoring work, How does accounts receivable f...

How does accounts receivable factoring work?  What are the benefits to the two parties involved?  What are the risks? Factoring is when one firm trade accounts receivable (AR)

Absolute performance standard, Absolute Performance Standard is a method of...

Absolute Performance Standard is a method of measuring an organization's development and how effective and efficient it is at operating its business. The absolute performance stand

Bond's capital gain yield, A 10-year, 12% semi-yearly coupon bond with a pa...

A 10-year, 12% semi-yearly coupon bond with a par value of $1,000 may be called in 4 years at a call price of $1,050. The bond sells for $1,050. (Suppose that the bond has just bee

Explain the post-acquisition effect on eps, Post-acquisition Effect on EPS...

Post-acquisition Effect on EPS If the consideration is completely in shares, one of the effects would be a dilution in EPS suffered by Predator Company. The effect of dilution

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd