Encyclopedic Dictionary of International Finance and Banking Phần 8 docx

Also, for any given expected return, most investors will prefer a lower risk, and for any given level of risk, they will prefer a higher return to a lower return.. What is important is t

A Methods for Dealing with Political Risk

To the extent that forecasting political risks is a formidable task, what can an MNC do

to cope with them? There are several methods suggested

countries that are considered to be of high risk and by using a higher discountrate for projects in riskier countries

• Adaptation—Try to reduce such risk by adapting the activities (for example, byusing hedging techniques)

• Diversification—Diversity across national borders, so that problems in one country

do not risk the company

• Risk transfer—Buy insurance policies for political risks Most developed nationsoffer insurance for political risk to their exporters Examples include: in the U.S.,the Eximbank offers policies to exporters that cover such political risks as war,currency inconvertibility, and civil unrest Furthermore, the Overseas Private Investment Corporation (OPIC) offers policies to U.S foreign investors to coversuch risks as currency inconvertibility, civil or foreign war damages, or expropri-ation In the U.K., similar policies are offered by the Export Credit Guarantee Department (ECGD); in Canada, by the Export Development Council (EDC); and

in Germany, by an agency called Hermes

EXAMPLE 99

Consider the following two-asset portfolio:

By changing the correlation coefficient, the benefits of risk reduction can be clearly observed,

as shown in Exhibits 90 and 91.

Wal-mart (US) 18.60% 22.80% 0.20 Smith-Kline (UK) 16.00% 24.00%

EXHIBIT 90 Portfolio Analysis Weight of

Wal-mart in Portfolio

Weight of Smith-Kline

in Portfolio

Expected Return (percent)

Expected Risk (percent)

See also DIVERSIFICATION; EFFICIENT PORTFOLIO; INTERNATIONAL CATION; PORTFOLIO INVESTMENTS; PORTFOLIO THEORY

DIVERSIFI-PORTFOLIO INVESTMENTS

1 Investing in a variety of assets to reduce risk by diversification An example of a portfolio

is a mutual fund that consists of a mix of assets which are professionally managed andthat seeks to reduce risk by diversification Investors can own a variety of securities with

a minimal capital investment Since mutual funds are professionally managed, they tend

to involve less risk To reduce risk, securities in a portfolio should have negative or nocorrelations to each other

See also DIVERSIFICATION; EFFICIENT PORTFOLIO; INTERNATIONAL

DIVERSIFI-CATION; PORTFOLIO THEORY

2 Investments that are undertaken for the sake of obtaining investment income or capital

gains rather than entrepreneurial income which is the case with foreign direct investments

(FDI ) This typically involves the ownership of stocks and/or bonds issued by public or

private agencies of a foreign country The investors are not interested in assuming control

of the firm

PORTFOLIO THEORY

Theory advanced by H Markowitz in attempting a well-diversified portfolio The central

theme of the theory is that rational investors behave in a way that reflects their aversion to

taking increased risk without being compensated by an adequate increase in expected return

Also, for any given expected return, most investors will prefer a lower risk, and for any given

level of risk, they will prefer a higher return to a lower return Markowitz showed how

quadratic programming could be used to calculate a set of “efficient” portfolios An investor

then will choose among a set of efficient portfolios the best that is consistent with the risk

profile of the investor

Most financial assets are not held in isolation but rather as part of a portfolio Therefore,

the risk–return analysis should not be confined to single assets only What is important is the

expected return on the portfolio (not just the return on one asset) and the portfolio’s risk

Most financial assets are not held in isolation; rather, they are held as parts of portfolios

Therefore, risk–return analysis should not be confined to single assets only It is important

to look at portfolios and the gains from diversification What is important is the return on

the portfolio (not just the return on one asset) and the portfolio’s risk

A Portfolio Return

The expected return on a portfolio (r p) is simply the weighted average return of the individual

sets in the portfolio, the weights being the fraction of the total funds invested in each asset:

where

rj = expected return on each individual asset

wj = fraction for each respective asset investment

n = number of assets in the portfolio = 1.0

EXAMPLE 100

A portfolio consists of assets A and B Asset A makes up one-third of the portfolio and has an

expected return of 18% Asset B makes up the other two-thirds of the portfolio and is expected

to earn 9% The expected return on the portfolio is:

Asset Return (r j) Fraction (w j) w j r j

where

σA and σB= standard deviations of assets A and B

wA and wB = weights, or fractions, of total funds invested in assets A and B

ρAB= the correlation coefficient between assets A and B

Incidentally, the correlation coefficient is the measurement of joint movement between twosecurities

C Diversification

As can be seen in the above formula, the portfolio risk, measured in terms of σ is not theweighted average of the individual asset risks in the portfolio We have in the formula a thirdterm (ρ), which makes a significant contribution to the overall portfolio risk What the formulabasically shows is that portfolio risk can be minimized or completely eliminated by diversi-fication The degree of reduction in portfolio risk depends upon the correlation between theassets being combined Generally speaking, by combining two perfectly negatively correlatedassets (ρ = −1.0), we are able to eliminate the risk completely In the real world, however,most securities are negatively, but not perfectly correlated In fact, most assets are positivelycorrelated We could still reduce the portfolio risk by combining even positively correlatedassets An example of the latter might be ownership of two automobile stocks or two housingstocks

EXAMPLE 101

Assume the following:

The portfolio risk then is:

(a) Now assume that the correlation coefficient between A and B is +1 (a perfectly positive relation) This means that when the value of asset A increases in response to market conditions,

so does the value of asset B, and it does so at exactly the same rate as A The portfolio risk when

(c) If ρ AB = −1 (a perfectly negative correlation coefficient), then as the price of A rises, the price

of B declines at the very same rate In such a case, risk would be completely eliminated fore, when ρ AB = −1, the portfolio risk is

There-σp= 0.0089 + 0.0089ρ AB = 0.0089 + 0.0089(−1) = 0.0089 − 0.0089 = 0 = 0 When we compare the results of (a), (b), and (c), we see that a positive correlation between assets increases a portfolio’s risk above the level found at zero correlation, while a perfectly negative correlation eliminates that risk.

Again, see that the two perfectly negative correlated securities (XY) result in a zero overall risk.

Year Security X (%) Security Y (%) Security Z (%)

D Markowitz’s Efficient Portfolio

Dr Harry Markowitz, in the early 1950s, provided a theoretical framework for the systematic

composition of optimum portfolios Using a technique called quadratic programming, he

attempted to select from among hundreds of individual securities, given certain basic mation supplied by portfolio managers and security analysts He also weighted these selec-tions in composing portfolios The central theme of Markowitz’s work is that rational investorsbehave in a way reflecting their aversion to taking increased risk without being compensated

infor-by an adequate increase in expected return Also, for any given expected return, most investorswill prefer a lower risk and, for any given level of risk, prefer a higher return to a lowerreturn Markowitz showed how quadratic programming could be used to calculate a set of

“efficient” portfolios such as illustrated by the curve in Exhibit 92

In Exhibit 93, an efficient set of portfolios that lie along the ABC line, called “efficientfrontier,” is noted Along this frontier, the investor can receive a maximum return for a givenlevel of risk or a minimum risk for a given level of return Specifically, comparing threeportfolios A, B, and D, portfolios A and B are clearly more efficient than D, because portfolio

A could produce the same expected return but at a lower risk level, while portfolio B wouldhave the same degree of risk as D but would afford a higher return

To see how the investor tries to find the optimum portfolio, we first introduce the indifferencecurve, which shows the investor’s trade-off between risk and return Exhibit 94 shows the two

EXHIBIT 92

Efficient Frontier

Efficient Frontierrp

different indifference curves for two investors The steeper the slope of the curve, the morerisk averse the investor is For example, investor B’s curve has a steeper slope than investorA’s This means that investor B will want more incremental return for each additional unit

Investor B

Investor A

Exhibit 95 depicts a family of indifference curves for investor A The objective is tomaximize his satisfaction by attaining the highest curve possible

By matching the indifference curve showing the risk–return trade-off with the best ments available in the market as represented by points on the efficient frontier, investors areable to find an optimum portfolio According to Markowitz, investor A will achieve the highestpossible curve at point B along the efficient frontier Point B is thus the optimum portfoliofor this investor

invest-E Portfolio Selection as a Quadratic Programming Problem

A portfolio selection problem was formulated by Markowitz as a quadratic programmingmodel as follows:

Minimize E(r p) − λV(rp)subject to

Σx i = 1, (i = 1, 2, … n)

x i≥ 0

where

E(r p) = the expected return

V(r p) = the variance or covariance of any given portfolio

x i = proportion of the investor’s total investment in security i

EXHIBIT 95

Matching the Efficient Frontier and Indifference Curve

A

B

n = number of securities

λ (Lamda) = coefficient of risk aversion

λ represents the rate at which a particular investor is just willing to exchange expectedrate of return for risk λ = 0 indicates the investor is a risk lover, while λ = 1 means he is arisk averter The resulting solution to the problem would identify a portfolio that lies on theefficient portfolio If one knows the coefficient of risk aversion, λ, for a particular investor,the model will be able to find the optimal portfolio for that investor

F The Market Index Model

For even a moderately sized portfolio, the formulas for portfolio return and risk requireestimation of a large number of input data Concern for the computational burden in derivingthese estimates led to the development of the following market index model:

r j = a + br m

where

r j = return on security j

r m = return on the market portfolio

b= the beta or systematic risk of a security

What this model attempts to do is measure the systematic or uncontrollable risk of a security.The beta is measured as follows:

where

Cov(r j , r m) = the covariance of the returns of the security with the market return

= the variance (standard deviation squared) of the market return, which isthe return on the Standard & Poor’s 500 or Dow Jones 30 Industrials

An easier way to compute beta is to determine the slope of the least-squares linear

regression line (r j − r f ), where the excess return of the security (r j − r f) is regressed against

the excess return of the market portfolio (r m − r f) The formula for beta is:

where M = (r m − r f ), K = (r j − r f ), n = the number of periods, = the average of M, and

= the average of K.

The market index model was initially proposed to reduce the number of inputs required

in portfolio analysis It can also be justified in the context of the capital asset pricing model

G The Capital Asset Pricing Model (CAPM)

The capital asset pricing model (CAPM) takes off where the efficient frontier concluded with

an assumption that there exists a risk-free security with a single rate at which investors canborrow and lend By combining the risk-free asset and the efficient frontier, we create a wholenew set of investment opportunities which will allow us to reach higher indifference curves

than would be possible simply along the efficient frontier The r f mx line in Exhibit 96 showsthis possibility This line is called the capital market line (CML) and the formula for this line is:

which indicates the expected return on any portfolio (r p ) is equal to the risk-free return (r f)plus the slope of the line times a value along the horizontal axis (σp) indicating the amount

of risk undertaken

H The Security Market Line

We can establish the trade-off between risk and return for an individual security through thesecurity market line (SML) in Exhibit 97 SML is a general relationship to show the risk–returntrade-off for an individual security, whereas CML achieves the same objective for a portfolio.The formula for SML is:

r j = r f + b(r m − r f)where

r j = the expected (or required ) return on security j

r f= the risk-free security (such as a T-bill)

r m= the expected return on the market portfolio (such as Standard & Poor’s 500 StockComposite Index or Dow Jones 30 Industrials)

b = beta, an index of nondiversifiable (noncontrollable, systematic) risk

This formula is called the Capital Asset Pricing Model (CAPM) The model shows that

investors in individual securities are only assumed to be rewarded for systematic,

uncontrol-lable, market-related risk, known as the beta (b) risk All other risk is assumed to be diversified

away and thus is not rewarded

The key component in the CAPM, beta (b), is a measure of the security’s volatility relative

to that of an average security For example, b = 0.5 means the security is only half as volatile,

or risky, as the average security; b = 1.0 means the security is of average risk; and b = 2.0 means the security is twice as risky as the average risk The whole term b(r m − r f) represents the riskpremium, the additional return required to compensate investors for assuming a given level of risk.Thus, in words, the CAPM (or SML) equation shows that the required (expected) rate of

return on a given security (r) is equal to the return required for securities that have no risk

(r f) plus a risk premium required by investors for assuming a given level of risk The higher

the degree of systematic risk (b), the higher the return on a given security demanded by investors Exhibit 97 shows the graph of the equation, known as the security market line (SML).

1 The price agreed upon between the purchaser and seller for the purchase or sale of an

option—purchasers pay the premium and sellers (writers) receive the premium

2 The excess of one futures contract price over that of another, or over the cash market price

PRIVATE EXPORT FUNDING CORPORATION

Private Export Funding Corporation (PEFCO) is a private U.S corporation, established withgovernment support, which helps finance U.S exports of big-ticket items from private sources.PEFCO purchases at fixed interest rates the medium- to long-term debt obligations of importers

of U.S products Foreign importer loans are financed through the sale of PEFCO’s ownsecurities Guarantees of repayment on all of PEFCO’s foreign obligations are provided by

the Eximbank.

PROJECT FINANCE LOAN PROGRAM

See EXPORT-IMPORT BANK

PUNT

Ireland’s currency

PURCHASING POWER PARITY (PPP)

Purchasing Power Parity (PPP) states that spot currency rates among countries will change

to the differential in inflation rates between countries There are two versions of this theory

Absolute PPP: The price of internationally traded commodities should be the same in

every country, that is, one unit of home currency should have the same purchasing power

worldwide The absolute version, popularly called the law of one price, is written as

where S = spot exchange rate in direct quotes (i.e., the number of units of home currency that can be purchased for one unit of foreign currency), P h = the price of the good in the

home country, and P f = the price of the good in the foreign country

Relative PPP: The relative version of purchasing power parity says that the exchange rate

of one currency against another will adjust to reflect changes in the price levels of the twocountries

Purchasing power parity can be summarized as follows:

Expected spot rate = current spot rate × expected difference in inflation rateMathematically,

- 1+I h

1+I

-=

where S1 and S2 = the spot exchange rate (direct quote) at the beginning of the period and the end of the period, I f = foreign inflation rate, measured by price indexes, and I h = home(domestic) inflation rate.

EXAMPLE 105

If the home currency experiences a 5% rate of inflation, and the foreign currency experiences a 2% rate of inflation, then the foreign currency will adjust by 2.94% (1.05/1.02 = 1.0294) In fact, the foreign currency is expected to appreciate by 2.94% in response to the higher rate of inflation

of the home country relative to the foreign country.

If purchasing power parity is expected to hold, then the best prediction for the one-period

spot rate, called the purchasing power parity (PPP) rate, should be:

(Equation 2)

A more simplified but less precise relationship of purchasing power parity is shown as:

(Equation 3)

Note: Dividing both sides of Equation 2 by S1 and then subtracting 1 from both sides yields

Equation 3 follows if I h is relatively small.

Equation 3 indicates that the exchange rate change during a period should equal the inflation differential for that same time period In effect, PPP says that currencies with high rates of inflation should devalue relative to currencies with lower rates of inflation.

EXAMPLE 106

If the home currency experiences a 5% rate of inflation, and the foreign currency experiences a 2% rate of inflation, the foreign currency should adjust by about 3% (5% − 2% = 3%)

Equation 3 is illustrated in Exhibit 98 The vertical axis shows the percentage appreciation

of the foreign currency relative to the home currency, and the horizontal axis measures the percentage higher or lower rate of inflation in the foreign country relative to the home country Equilibrium is reached on the parity line, which contains all those points at which these two differentials are equal At point A, for example, the 3% inflation differential is exactly offset by the 3% appreciation of the foreign currency relative to the home currency Point B, on the other hand, portrays a situation of disparity, where the inflation differential of 3% is greater than the appreciation of 1% in the home currency value of the foreign currency.