# Tracking KLSE Counters

## Friday, May 29, 2015

## Thursday, November 15, 2012

### Bond Portfolio Management

__THE LEVEL OF MARKET INTEREST RATES__**Numerous interest rates exist and they vary continuously. The market rate of interest (or nominal rate) for a security can be expressed symbolically as follows:**

Equation 1.1

Nominal interest rate (r)

= real interest rate (rr) + expected rate of inflation (q) + various risk premiums (rp)

The real interest rate is

__the rate at which physical capital is expected to reproduce in an economy.__Since suppliers of funds expect to be compensated for inflation, the

__expected rate of inflation__over the life of the asset should be added to the real rate.

__Adjustments__to a bond's yield-to-maturity (YTM) are also made for the

__following risk factors:__

*This is the*

__(1) Default risk.____risk of bankruptcy__and, therefore, the inability of a corporation to pay the contractual interest on debt.

*The risk of not being able to*

__(2) Liquidity risk.____sell an asset quickly at full value.__

*The fluctuation in price,*

__(3) Interest-rate risk.____especially for long-term bonds,__from changes in the interest rate. Also included

__reinvestment rate risk.__

*The risk of*

__(4) Foreign-exchange risk.____holding bonds in a foreign currency.__

Some other factors affecting YTM are

__taxes and issue characteristics__. Municipal bond coupons are exempt from federal taxes and, therefore, have lower interest rates than taxable corporate bonds. Special features in a bond's indenture such as an

__embedded call or put__can influence its yield.

__Currently, T-bills with a maturity of 13 weeks have a YTM lower than long-term T-bonds yields. Using Equation 1.1, explain why these returns differ.__Two factors given in Equation 1.1 could account for the differences. They are (1) inflationary expectations and (2) interest-rate risk. Since long-term bonds have several more years to maturity than T-bills, expectations for higher rate of inflation in the future could account for some of the differential. In addition, long-term bonds have more interest-rate risk than short-term bonds and, therefore, a greater risk premium is required.

__Long-term BBB-rated corporate bonds yield more than AAA-rated corporate bonds with the same maturity. Explain in terms of Equation 1.1.__If we assume both issues have identical characteristics, then the main reason the BBB-rated bonds have a higher return is greater default risk than AAA-rated bonds.

__Several times in U.S. financial history short-term securities such as commercial paper have had a higher return than long-term bonds (both T-bonds and corporates). Explain how this could happen with Equation 1.1.__The main factor must be decreasing inflationary expectations. If the rate of inflation is expected to fall in the future this makes the expected average rte of inflation smaller for long-term bonds than short-term securities. For example, the lower rate of inflationary expectations more than offsets the higher default risk and interest-rate risk associated with long-term corporate bonds.

__YIELD SPREADS__*Yield spreads*are the

__differences in yields between risky bonds and default-free U.S. Treasury bonds of similar maturity.__This equation below defines the yield spread for the

*t*th time period.

Equation 1.2

(Yield spread)t

= (yield on risky bond)t - (yield on a U.S Treasury bond)t

**Example**

Suppose an AAA-grade corporate bond's current YTM is 11% while the YTM on a similar T-bond is 9%. Equation 1.2 suggests the yield spread for the pair of bonds is 2% or 200 basis points.

Yield spreads tend to

__vary__over the business cycle. They are

__larger__at business

__troughs than at peaks,__and yield spreads take place in a

__predictable fashion.__

__As a result, bond traders and investors who can act quickly when yield spreads appear to be different from normal can make profits.__**Example**

Tom, an astute bond trader, noted that the yield spread between a BBB-rated corporate bond issue and a similar T-bond issue was 250 basis points. However, according to Jeff's careful analysis, the normal yield spread for the two bonds for this stage of the business cycle should be 200 basis points. Jeff feels that he can profit from the abnormal yield spread.

In order for the yield spread to become normal it must decrease. For this to happen, either the BBB corporate bonds must increase in price (yields fall) or the T-bonds must fall in price (yields increase). Therefore, Tom should purchase the BBB bonds. If, as is likely, the BBB bonds increase in price, he would profit.

__TERM STRUCTURE OF INTEREST-RATE THEORIES__The relationship at a point in time between the YTMs of homogenous bonds and the years to maturity for the bonds, holding other things constant, is called the

__term structure of interest rates or yield curve.____Three main explanations or theories__of the term structure have been given. An explanation of each one of these hypotheses is presented below.

**The Expectations Hypothesis**The expectations approach to the term structure of interest rates states that long-term interest rates are the geometric mean of expected forward (or future) short-term interest rates.

__The Liquidity Premium Hypothesis__While the expectations approach to the term structure of interest rates implies a flat yield curve if interest rates are not expected to change in the future, the

*under similar circumstances, implies a*

__liquidity preference theory,____rising yield curve.__According to the liquidity preference theory, investors demand a risk premium from long-term securities. As long-term bonds have more interest-rate risk, investors require higher returns.

__The Segmentation Hypothesis__According to the

*, certain investors and financial institutions prefer to invest in certain segments of the yield curve. For example, due to the stable long-term nature of their liabilities,*

__segmented market theory____pension funds prefer to invest in long-term securities.__On the other hand,

__commercial banks' short-term liabilities (namely, demand deposits) create a need for short-term assets.__

__As a result, supply and demand for funds within each segment of the market determine the level and structure of interest rates for that segment.__

__BOND PORTFOLIO IMMUNIZATION__**The interest-rate risk from coupon-paying bonds is composed of two components:**

(1) price risk and

(2) coupon reinvestment rate risk.

These two components of interest-rate risk

*vary inversely.*If a bond investor wants the promised YTM and the realized YTM to remain equal over the life of a coupon bond,

__interim interest payments must be invested at the promised YTM.__If interim rates change, the realized YTM can be either greater or less than the promised YTM.

__One way to assure the bond investor that the portfolio held will achieve the desired realized yield is to immunize the portfolio.__

*For example, immunizing a portfolio for 5 years requires the purchase of a series of bonds with an*

__Immunization takes place when the desired holding period of the portfolio equals the bond portfolio's Macaulay's duration.____average Macaulay's duration of 5 years, not an average maturity of 5 years.__

__Immunization achieves this result because reinvestment risk and price risk exactly offset one another whenever a bond portfolio's desired holding period is equal to its duration.__There are limitations to immunization.

*Duration tends to diminish more slowly than calendar time for coupon-paying bonds when interest rates do not change.*

__Every time market interest rates change the duration of every bond changes.____Therefore, periodic rebalancing will be necessary to continuously immunize a portfolio of bonds.__In addition, yield curves are not necessarily flat and do not shift in a parallel fashion, so the use of duration will not be exact.

**Learning Points:**

One of the problems with immunization is the

__cost__associated with rebalancing.

According to the expectations approach to the term structure of interest rates, a falling yield curve

__forecasts__falling interest rates in the years ahead.

Yield spreads tend to

__narrow__during a boom period in the economy.

The average duration for a portfolio of zero coupon bonds will

__change__as interest rates change.

If the interest rate is 10%, the weighted average duration for a portfolio of two $40 million face value zero coupon bonds with maturities of 4 and 8 years, respectively, is 5.64 years.

The liquidity preference theory about the term structure of interest rates asserts that if short-term interest rates are expected to remain the same in the future, the yield curve should be a

__rising__yield curve.

Long-term bonds have

__more__price change risk than short-term bonds.

## Wednesday, November 14, 2012

### Bond Valuation

__BOND VALUES__The value of a bond is simply the present value of all the security's future cash flows, as show below.

__Basic Bond Equation:__Present value

= [COUPON1/((1+YTM)^1)] + [COUPON2/((1+YTM)^2)] + .....+ [(COUPONt + face value)/((1+YTM)^t)]

The four terms that appear on the right-hand side of the present-value equation are discussed below:

__(1) Market interest rate:__The discount rate, or interest rate or yield-to-maturity, is the market interest rate that constantly changes. The bond's yield-to-maturity is represented by the symbol YTM. The YTM is the discount rate that equates all the bond's future cash flows with the current market price of the bond.

__(2) Face value, F:__The bond's face value (or principal value) is printed on the bond and is invariant throughout the bond's life.

__(3) Coupon:__The dollar amount of a bond's coupon interest payments equals the product of the coupon interest rate, denoted i, and the face value, F. Symbolically, coupon = iF.

__(4) The number of time periods__left until the bond matures and the terminal payment occurs is denoted T.

**Example:**

What is the value of a $1,000 bond with an 8% coupon rate, 3 years before maturity? The YTM is 10%.

iF = (0.08)($1,000) = $80

T = 3

YTM = 10

Present value

= [$80/((1+0.10)^1)] + [$80/((1+0.10)^2)] + [($80 + $1000)/((1+0.10)^3)]

= $72.727 + $66.116 + $811.420

= $ 950.26

__Semiannual Coupon Payments__**Semiannual coupon payments are more common than annual coupons. Therefore, the present value of a bond model must be modified slightly to accommodate the semiannual coupon payments.**

**Example:**

A $1,000 bond with an 8% coupon rate, 3 years before maturity. The YTM is 10%. What is the bond's present value if the coupons are paid semiannually?

Converting annual compounding to the semiannual compounding model for the same bond. The bond's annual coupon payments must be halved to get the semiannual coupon payments. The bond's compounding period is 6 months. The appropriate market rate of return or discount rate for semiannual coupons is half of the bond's YTM.

Coupon Payment iF = (0.08)($1,000) = $ 80

Semiannually Coupon Payment = 0.5 x iF = (0.08/2)($1,000) = $ 40

T = 3 years

2T = 6 semiannual periods

YTM = 10%

Semiannual discount rate = YTM/2 = 10%/2 = 5%.

The present value of the bond will be the

*for the 8% coupon bond maturing in 6 six-month periods. Note that*

__asked price____using the more frequent compounding interval__

*the present value of the bond when compared with the bond with annual coupon payments.*

__reduced__

__Accrued Coupon Interest__Accrued interest is interest that has been earned by an investor but that has not yet been paid to that investor.

__Bond buyers pay bond sellers__Thus, if a bond were sold between its semiannual interest payment dates, the purchaser should pay the market price of the bond

*accrued interest*whenever a bond is purchased on a date that is not a scheduled coupon interest payment date.*but not yet received by the party selling the bond.*

__plus the appropriate fraction of the accrued coupon interest earned__**Example:**

What is the purchase price for a bond that is paying a 6% annual coupon rate in semiannual payments if its YTM=10.0% and it has 2 years and 10 months from its purchase date until its maturity? What is the accrued interest? Assume the bond is traded in a year of 366 days when calculating the accrued interest.

**Solution:**

Since this bond has 2 months short of 3 full years until it matures, we must first

__- (Step one)__calculate its present value on the next interest payment date, which is 2.5 years until maturity. After the present value of a 2.5 year bond has been calculated,

__- (Step two)__we will add the interest payment received on that date to the price of the bond.

__- (Step three)__Next, the value determined in Step two should be discounted back 4 months to the purchase date.

__Yield-to-Call__Sometimes the issuer of a bond has the option to call (or redeem) the bond before it reaches maturity. This is likely to occur when the coupon interest rate on similar new bonds is substantially below the coupon interest on existing bonds because the corporation can save money on future interest payments.

__When a bond has an excellent chance of being called, an investor may want to calculate the yield-to-call for the bond.__This can be accomplished by modifying the basic bond equation, in the following manner:

- T would now equal the
and*number of time periods until the bond is called,* - Face value would now be the
__call value.__

__BOND DURATION__**Macaulay's duration (MD) is the average time it takes to receive the cash flows expected from a bond or another asset.**

The table below shows the relationship between Macaulay's duration (MD) and years-to-maturity for semiannual bonds of various coupon rates that have YTM of 9%.

A bond's duration is

__less than__its year-to-maturity for coupon bonds.

MD

__equals__T for zero coupon bonds.

MD also increases at a decreasing rate as maturity increases for bonds selling at par or above.

For discount bonds, note that duration will eventually

__decline.__

**Table: Macaulay's Duration (in Years) for Bond Yielding 9 Percent (Semiannual Compounding)**

Coupon | ||||||||

Rate | 3% | 6% | 9% | 12% | ||||

Year to | ||||||||

Maturity | ||||||||

5 | 4.622 | 4.345 | 4.134 | 3.968 | ||||

10 | 8.249 | 7.347 | 6.797 | 6.426 | ||||

20 | 12.272 | 10.437 | 9.615 | 9.148 | ||||

50 | 12.391 | 11.703 | 11.469 | 11.35 | ||||

70 | 11.832 | 11.648 | 11.587 | 11.586 | ||||

100 | 11.366 | 11.616 | 11.609 | 11.606 | ||||

Infinity | 12.111 | 12.111 | 12.111 | 12.111 | ||||

The relationship between a change in the price of a bond relative to a change in its YTM is usually referred to as

*(MMD) for a bond.*

__modified duration__

__Learning Points:__Duration for a zero coupon bond is the

__same__as its term to maturity.

Shorter-term bonds are almost always

__more volatile in terms of price__than longer-term bonds for a given

__change in interest rates.__

Bond price volatility is

__inversely__related to the bond's coupon.

Duration of a coupon-paying bond is always

__less than__its term to maturity.

For any given maturity, bond price movements that result from an equal absolute decrease or increase in the yield-to-maturity are

__asymmetrical.__

There is an

__inverse__relationship between a bond's coupon and duration.

As a bond's YTM increases, if other things are held constant, its duration

__decreases.__

The duration for a perpetual bond is

__finite.__

When a bond is selling at a discount, its YTM

__exceeds__the coupon rate.

When a bond's YTM equals its coupon rate, the bond's price is

__more than__par value.

## Tuesday, November 13, 2012

### Portfolio Analysis

Total risk of an individual asset is measured by the standard deviation (or variance) of returns of the asset.

Let's look at the relationship between the risk and return for a portfolio of assets. For a portfolio of assets, the return on a portfolio is simply the sum of the individual assets, its risk is not simply the sum of the risk of the single assets. When a portfolio's standard deviation is calculated, attention must be given to the covariance of the returns of the assets. Harry Markowitz has shown that portfolios dominate individual assets from a risk and return standpoint. He also showed how the optimal portfolio could be determined.

The covariance is a statistical measure of how the returns of two assets move together.

The correlation is also a measure of the relationship between two assets. The correlation coefficient can take on a value from -1 to +1. Correlation and covariance are related by the following equation:

COVij = DiDjPij

Di and Dj are the standard deviations of returns for assets i and j

Pij is the correlation coefficient for assets i and j.

The return on a portfolio of assets is simply the weighted average return.

A portfolio of 4 common stocks with the following market values and returns:

STOCK MARKET VALUE STOCK RET.

X $10,000 10%

Y 20,000 14%

Z 30,000 16%

M 40,000 15%

_______

100,000

The return on this portfolio is determined thus:

Rp

= ($10,000/$100,000)(10) + ($20,000/$100,000)(14) + $30,000/$100,000)(16) + ($40,000/$100,000)(15)

= (0.1)(10) + (0.2)(14) + (0.3)(16) + (0.4)(15)

= 1 + 2.8 + 4.8 + 6)

= 14.6%

The variance of returns for a portfolio of assets can be calculated using a general formula.

A two-asset portfolio can be used to illustrate some of the principles of diversification.

Portfolio theory suggests that as the correlation coefficient declines risk should decline, but the portfolio's expected return should not vary, if the weights of the assets are held constant. The important point is that if assets are less than perfectly positively correlated (that is, a correlation coefficient below +1), diversification can reduce risk.

The A and B Corporations have the following expected risk and return inputs for next year:

Er(A) = 18% Er(B) = 22%

SD(A) = 22% SD(B) = 30%

A 25% reduction in risk is (0.25)(21.8632%) = 5.4658%. Therefore, the new level of risk will be 21.8632% - 5.4658% = 16.3974%.

Correlation coefficient = -0.2337

Answer:

Expected return = 20%

If we consider the infinite number of portfolios that could be formed from two or more securities and plotted these portfolios' expected return and risk, we would create graphs like so.

The efficient frontier is represented by the curve line. Portfolios along this line dominate all other investment possibilities. The highest return portfolio(on the far right of the curve) is the only one that is likely a one-asset portfolio. The curvature of the efficient frontier depends upon the correlation of the asset's returns. The efficient frontier curve is convex toward the expected return axis because all assets have correlation coefficients that are less than positive unity and greater than negative unity.

Given the above assumptions, an investor will want to hold a portfolio somewhere along the efficient frontier. The exact location depends on the investor's risk-return preferences. A set of indifference curves for each investor will show his or her risk-return tradeoff. Those investors with more risk-aversion require more compensation for assuming risk and will choose a portfolio along the lower end of the efficient frontier. The portfolio will be optimal because no other portfolio along the efficient frontier can dominate another in terms of risk and return.

Let's look at the relationship between the risk and return for a portfolio of assets. For a portfolio of assets, the return on a portfolio is simply the sum of the individual assets, its risk is not simply the sum of the risk of the single assets. When a portfolio's standard deviation is calculated, attention must be given to the covariance of the returns of the assets. Harry Markowitz has shown that portfolios dominate individual assets from a risk and return standpoint. He also showed how the optimal portfolio could be determined.

**COVARIANCE OF RETURNS**The covariance is a statistical measure of how the returns of two assets move together.

**CORRELATION**The correlation is also a measure of the relationship between two assets. The correlation coefficient can take on a value from -1 to +1. Correlation and covariance are related by the following equation:

COVij = DiDjPij

Di and Dj are the standard deviations of returns for assets i and j

Pij is the correlation coefficient for assets i and j.

**PORTFOLIO RETURN**The return on a portfolio of assets is simply the weighted average return.

__Example:__A portfolio of 4 common stocks with the following market values and returns:

STOCK MARKET VALUE STOCK RET.

X $10,000 10%

Y 20,000 14%

Z 30,000 16%

M 40,000 15%

_______

100,000

The return on this portfolio is determined thus:

Rp

= ($10,000/$100,000)(10) + ($20,000/$100,000)(14) + $30,000/$100,000)(16) + ($40,000/$100,000)(15)

= (0.1)(10) + (0.2)(14) + (0.3)(16) + (0.4)(15)

= 1 + 2.8 + 4.8 + 6)

= 14.6%

**PORTFOLIO STANDARD DEVIATION**The variance of returns for a portfolio of assets can be calculated using a general formula.

**TWO-ASSET CASE**A two-asset portfolio can be used to illustrate some of the principles of diversification.

Portfolio theory suggests that as the correlation coefficient declines risk should decline, but the portfolio's expected return should not vary, if the weights of the assets are held constant. The important point is that if assets are less than perfectly positively correlated (that is, a correlation coefficient below +1), diversification can reduce risk.

The A and B Corporations have the following expected risk and return inputs for next year:

Er(A) = 18% Er(B) = 22%

SD(A) = 22% SD(B) = 30%

*The portfolio risk (standard deviation) for a portfolio of 50% in each asset is 21.8632 percent. Determine the correlation coefficient that will be necessary to reduce the level of portfolio risk by 25%.*__Answer:__A 25% reduction in risk is (0.25)(21.8632%) = 5.4658%. Therefore, the new level of risk will be 21.8632% - 5.4658% = 16.3974%.

Correlation coefficient = -0.2337

*What is the expected return of the equally weighted portfolio?*Answer:

Expected return = 20%

**EFFICIENT FRONTIER**If we consider the infinite number of portfolios that could be formed from two or more securities and plotted these portfolios' expected return and risk, we would create graphs like so.

The efficient frontier is represented by the curve line. Portfolios along this line dominate all other investment possibilities. The highest return portfolio(on the far right of the curve) is the only one that is likely a one-asset portfolio. The curvature of the efficient frontier depends upon the correlation of the asset's returns. The efficient frontier curve is convex toward the expected return axis because all assets have correlation coefficients that are less than positive unity and greater than negative unity.

**OPTIMUM PORTFOLIO**- Markowitz portfolio analysis makes the following assumptions:
- The investor seeks to maximise the expected utility of total wealth.
- All investors have the same expected single period investment horizon.
- Investors are risk-averse.
- Investors base their investment decisions on the expected return and standard deviation of returns from a possible investment.
- Perfect markets are assumed (e.g. no taxes and no transaction costs).

Given the above assumptions, an investor will want to hold a portfolio somewhere along the efficient frontier. The exact location depends on the investor's risk-return preferences. A set of indifference curves for each investor will show his or her risk-return tradeoff. Those investors with more risk-aversion require more compensation for assuming risk and will choose a portfolio along the lower end of the efficient frontier. The portfolio will be optimal because no other portfolio along the efficient frontier can dominate another in terms of risk and return.

### International Investing - "Why not diversify Internationally rather than Domestically?"

With over half of the market value of stocks and bonds outside the U.S., international investing is

It is possible to

There are tables showing the

Countries have different political systems, different customs, different regulations governing trade and business, and cultural differences. In addition, some countries are experiencing internal conflicts. Furthermore, some countries may have high inflation while other countries may be experiencing low inflation, or some may be having a booming economy, while others may be experiencing a recession.

While international investing can reduce risk below domestic levels, one important risk factor was not considered -

Bought US $1,000 worth of Australian stock and hold it for 1 year.

Current exchange rate is US $1 dollar for 1 Australian dollar (AD).

Therefore, this purchased stock worth AD 1,000.

Australian stock return 10%.

Exchange rate at end of the year was US$0.90 /AD 1/

Returns from a U.S. perspective was as follows:

1. Convert the Australian investment into US dollars.

1,000 x 1.1 = AD 1,100 (ending investment with 10% growth) x US$90 = US$990

The net return can be calculated with the following equation:

Rn = (1+Rd) (!+Rc) - 1

Net return = (1 + foreign security's return) (1 + currency return) - 1

The investors can do something about exchange rate.

Mr. A is planning to purchase a gilt, a British government bond, with an annual yield-to-maturity of 9%. Currently, the exchange rate is $1.80 per pound sterling, and the 1-year forward exchange rate is $1.90 per pound. If Mr. A hedges his position, what annual return can he lock in with the British bills (ignoring transaction costs)?

Mr. A makes two investments, one in a British government bond and the other in the British pound. The British bill will earn a riskless 9%. Her currency investment will yield 5.56%.

$1.90/$1.80 - 1 = 1.056 - 1 = 0.0556 = 5.56%

The combined net return that is locked in, is,

Rn = (1 + Rd) (1+Rc) -1

= (1.09) (1.0556) - 1

= 1.1506 -1

= 0.1506

= 15.06%.

__important as a way to improve returns and lower risk.__It is fairly easy to invest internationally today through open-end international mutual funds.**INTERNATIONAL DIVERSIFICATION**It is possible to

__reduce risk__*below*the level in domestic markets by diversifying internationally.There are tables showing the

__These correlations are in most cases lower than the correlation between large portfolios of domestic stocks. The__*correlation matrix of returns for the stock indexes*of various countries.__international correlation of stock returns encourages multinational investing because it allows an investor to__*lower*__reduce risk even further.____Why are the international correlation coefficients lower than the correlation between domestic stocks?__Countries have different political systems, different customs, different regulations governing trade and business, and cultural differences. In addition, some countries are experiencing internal conflicts. Furthermore, some countries may have high inflation while other countries may be experiencing low inflation, or some may be having a booming economy, while others may be experiencing a recession.

__All these factors tend to cause the correlation of security returns between countries to be__*lower*than the correlation of returns between securities (or groups of securities) in the domestic economy.__FOREIGN EXCHANGE RISK__While international investing can reduce risk below domestic levels, one important risk factor was not considered -

__When investing in another country the investor must convert domestic currency into a foreign currency. Then, when the foreign investment is terminated, the process must be reversed.__*foreign exchange risk.*__In essence, two investments are made.____One investment is in the__*foreign security*and the other is in that*foreign country's currency.*__Example 1:__Bought US $1,000 worth of Australian stock and hold it for 1 year.

Current exchange rate is US $1 dollar for 1 Australian dollar (AD).

Therefore, this purchased stock worth AD 1,000.

Australian stock return 10%.

Exchange rate at end of the year was US$0.90 /AD 1/

Returns from a U.S. perspective was as follows:

1. Convert the Australian investment into US dollars.

1,000 x 1.1 = AD 1,100 (ending investment with 10% growth) x US$90 = US$990

*The positive 10% return from the Australian investment, but the loss on the foreign currency investment more than offset the gain from the Australian security.*The net return can be calculated with the following equation:

Rn = (1+Rd) (!+Rc) - 1

Net return = (1 + foreign security's return) (1 + currency return) - 1

The investors can do something about exchange rate.

__An investor could lock in a fixed return by purchasing the appropriate forward contract on the foreign currency.__For the hedge to work properly, however, the investor needs to know exactly how much foreign currency to sell in the forward market.__Example 2__Mr. A is planning to purchase a gilt, a British government bond, with an annual yield-to-maturity of 9%. Currently, the exchange rate is $1.80 per pound sterling, and the 1-year forward exchange rate is $1.90 per pound. If Mr. A hedges his position, what annual return can he lock in with the British bills (ignoring transaction costs)?

Mr. A makes two investments, one in a British government bond and the other in the British pound. The British bill will earn a riskless 9%. Her currency investment will yield 5.56%.

$1.90/$1.80 - 1 = 1.056 - 1 = 0.0556 = 5.56%

The combined net return that is locked in, is,

Rn = (1 + Rd) (1+Rc) -1

= (1.09) (1.0556) - 1

= 1.1506 -1

= 0.1506

= 15.06%.

__This type of hedge will work__because Mr. A knows exactly how many pounds sterling he will have from the riskless British government bond at the end of the year.__If his investment had been in the risky British equity market, he would have been uncertain about the investment's outcome__and, as a result, uncertain about the number of pounds he would have at the end of the year.__Learning Points:__- International investing offers the individual investor the potential to reduce risk
__below__the level in the domestic market. - Exchange rate risk
__cannot__be eliminated by hedging in the forward foreign exchange market. - An efficient frontier that is constructed with international equities usually
__dominates__one constructed only with domestic equity securities. - Exchange rate risk is
__a problem__when investing in international equities and international bonds. - The majority of international equity indexes have betas
__less than 1__when their returns are regressed with the returns of the S&P500 index. - If an investor buys a British security, the investor's return will
__not be the same__whether the investment is made in dollars or pound sterling. - If you invest in a British corporation and earn a 12% rate of return on your British investment, this return will be
__enhanced__from the Malaysian perspective if the Malaysian ringgit__decreases__in value relative to the British pound. - An American investing in Japan would be
__happy__if the dollar__depreciated__in value relative to the yen, but a Japanese investing in the U.S.__would not__. - Even though a U.S. and British investor may experience
__identical returns__from an investment in France, from the perspective of their particular currencies, their returns will most likely__differ.__

### Portfolio Performance Evaluation

__MUTUAL FUNDS__Investment companies come in two forms. The

__open-end__investment company, or as it is usually called a mutual fund, is the most common type of investment fund.

__Closed-end__funds, the second type of investment company, are not as popular as the open-end funds.

__Unlike the open-end funds, closed-end funds cannot sell more shares after the initial public offering.__Stocks and bond mutual funds can be classified into various categories such as

*Mutual funds offer*

__growth funds, balanced funds, income funds, government bond funds, junk bond funds, and international funds.____small investors the ability to diversify__for lower commission costs and lower management fees than most alternatives.

Most of the empirical evidence to date indicates that most mutual funds

__do not beat the market,__after adjustments are made in their returns for transaction costs and risk.

__Net Asset Value per Share__A mutual fund's

__net asset value per share (NAV)__is equal to the total market value of all the mutual fund's holdings minus liabilities divided by the fund's total number of outstanding shares on

__a particular day.__

__One-Period Rate of Return__A mutual fund's one-period rate of return can be calculated with the following equation:

Rt = [Ct + Dt + (NAVt - NAVt-1)] / NAVt-1

Rt = The fund's return for time period t

Ct = The capital gains disbursement during time period t

Dt = The cash dividend or interest disbursement during time period t

NAVt = The fund's net asset value per share at the end of time period t

NAVt-1 = The fund's net asset value per share at the end of time period t+1

(NAVt - NAVt-1) = The change in the fund's net asset value per share from the beginning of time period t until the end of time period t [or, equivalently, the beginning of period (t-1)], as the result of capital gains and cash dividends that were not distributed to the owners during time period t.

__GEOMETRIC MEAN RETURN__There are two important aspects of any investment that must be evaluated over the investment's holding period - the return and the risk.

*The geometric mean rate of return for an investment can be calculated with the following equation:*

__The multiperiod (or compounded) rate of return is called the geometric mean return.__GMR = [(1+R1)(1+R2)(1+R3) ...(1+Rt) -1]^(1/t)

GMR = The geometric mean return

R1 = The return for the time period 1

R2 = The return for the time period 2

Rt = The return for time period T

T = The total number of time periods

The annual returns over the past 5 years are given below for the company XYZ:

Year Return

1991 10%

1992 12%

1993 15%

1994 13%

1995 16%

The geometric mean rate of return for the company XYZ over the past 5 years is:

GMR

= [(1.10)*(1.12)*(1.15)*(1.13)*(1.16) - 1 ] ^ (1/5)

= 1.131798

= 13.18%

__Other Performance Measures__SHARPE'S PERFORMANCE MEASURE

JENSEN'S PERFORMANCE MEASURE

COMPARISON OF PERFORMANCE MEASURES

__COMPARISON OF PERFORMANCE MEASURES__The Sharpe portfolio performance measure is based on the capital market line (CML) and total risk, which makes it

__more suitable for evaluating portfolios rather than individual assets.__On the other hand, both the Jensen and Treynor performance measures are based on the capital asset pricing model (CAPM) and are more flexible because by using systematic risk (beta) they can be

__used to evaluate the performance of both portfolios and individual assets.__All three performance measures tend to rank a group of diversified portfolios similarly.

__Learning points:__- Most growth-oriented mutual funds
__do not outperform__the S&P 500 on a risk-adjusted basis. - The Treynor performance measure is
__better__than the Sharpe performance measure for evaluating the performance of__individual common stocks.__ - The
__compounded rate of return__is another name for the__geometric mean rate of return.__ - The geometric mean rate of return for an asset will always be
__smaller__than its arithmetic mean rate of return. - Most empirical studies of mutual funds report that the funds
__did not consistently do better__than the market average. - One good way for small investors to
__diversify__their holdings is to purchase mutual funds. - After its initial offering, a closed-end mutual fund
__cannot__sell more shares. - The internal rate of return (IRR) should be used only with investments for which the size and timing of the cashflows are determined
__endogenously__(for example, cashflows from an investment in a manufacturing machine). - The geometric mean return (GMR) should be used for investments in which the cashflows are
__exogenously__determined (for example, investor deposits and withdrawals from a mutual fund).

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