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Investment Analysis and Portfolio Management

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Investment Analysis & Portfolio Management (FIN630)
VU
Lesson # 32
UNDERSTANDING RISK AND RETURN Contd...
RISK:
It is not sensible to talk about investment returns without talking about risk, because
investment decisions involve a trade-off between the two--return and risk are opposite
sides of the same coin. Investors must constantly be aware of the risk they are assuming,
know what it can do to their investment decisions, and be prepared for the consequences.
Investors should be "willing to purchase a particular asset if the expected return is, adequate
to compensate for the risk, but they must understand that their expectation about the asset's
return may not materialize. If not, the realized return will differ from the expected return. In
fact, realized returns on securities show considerable variability sometimes they are larger
than expected, and other times they are smaller than expected, or even negative. Although
investors may receive their expected returns on risky securities on a long-run average basis,
they often fail to do so on a short-run basis.
SOURCES OF RISK:
What makes a financial asset risky? Traditionally, investors have talked about several
sources of total risk, such as interest rate risk and market risk, which are explained
below, because these terms are used so widely, Following this discussion, we will define the
modern portfolio sources of risk, which will be used later when we discuss portfolio and
capital market theory.
1. Interest Rate Risk:
The variability in a security's return resulting from changes in the level of interest rates is
referred to as interest rate risk. Such changes generally affect securities inversely; that is,
other things being equal, security prices move inversely to interest rates. Interest rate risk
affects bonds more directly than common stocks, but it affects both and is a very important
consideration for most investors.
2. Market Risk:
The variability in returns resulting from fluctuations in the overall market that is, the
aggregate stock market is referred to as market risk. All securities are exposed to market
risk, although it affects primarily common stocks.
Market risk includes a wide range of factors exogenous to securities themselves, including
recessions, wars, structural changes in the economy, and changes in consumer preferences.
3. Inflation Risk:
A factor affecting all securities is purchasing power risk, or the chance that the purchasing
power of invested dollars will decline/With uncertain inflation, the real (inflation-adjusted)
return involves risk even if the nominal return is safe (e.g., a Treasury bond). This risk is
related to interest rate risk, since interest rates generally rise as inflation increases, because
lenders demand additional inflation premiums to compensate for the loss of purchasing
power.
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Investment Analysis & Portfolio Management (FIN630)
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4. Business Risk:
The risk of doing business in a particular industry or environment is called business risk.
For example, AT&T, the traditional telephone powerhouse, faces major changes today in
the rapidly changing telecommunications industry.
5. Financial Risk:
Financial risk is associated with the use of debt financing by companies. The larger the
proportion of assets financed by debt (as opposed to equity), the larger the variability in the
returns, other things being equal. Financial risk involves the concept of financial leverage,
which is explained in managerial finance courses.
6. Liquidity Risk:
Liquidity risk is the risk associated with the particular secondary market in which a security
trades. An investment that can be bought or sold quickly and without significant price
concession is considered to be liquid. The more uncertainty about the time element arid the
price concession, the greater the liquidity risk. A Treasury bill has little or no liquidity risk,
whereas a small over-the-counter (OTC) stock may have substantial liquidity risk.
7. Exchange Rate Risk:
All investors who invest internationally in today's increasingly global investment arena face
the prospect of uncertainty in the returns after they-convert the foreign gains back to their
own currency Unlike the past when most U.S. investors ignored international investing
alternatives, investors today must recognize and understand exchange rate risk, which can
be defined as the variability in returns on securities caused by currency fluctuations.
Exchange rate risk is sometimes called currency risk.
For example, a U.S. investor who buys a German stock denominated in marks must
ultimately convert the returns from this stock back to dollars. If the exchange rate has
moved against the investor, losses from these" exchange rate' movements can partially or
totally negate the original return earned.
8. Country Risk:
Country risk, also referred to as political risk, is an important risk for investors today
probably more important now than in the past. With mote investors investing
internationally, both directly and indirectly, the political, and therefore economic, stability
and viability of a country's economy need to be considered. The United States arguably has
the lowest country, risk, and other countries can be judged on a-relative basis using the
United States as a benchmark. Examples-of countries that needed careful monitoring in the
1990s because of country risk included the, former Soviet Union ^and Yugoslavia, China,
Hong Kong, and Smith Africa. In the-early part of the twenty-first century, several countries
in South America, Turkey, Russia, and Hong Kong, among others, require careful attention.
TYPES OF RISK:
Thus far, our discussion has concerned the total risk of an asset, which is one important
consideration in investment analysis. However, modern investment analysis categorizes the
traditional sources of risk identified previously as .causing variability in returns into two
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Investment Analysis & Portfolio Management (FIN630)
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general types: those that are pervasive in nature, such as market risk or interest rate risk, and
those that are specific to a particular security issue, such as business or financial risk.
Therefore, we must consider these two categories of total risk.
Dividing total risk into its two components, a general (market) component and a
specific (issuer) component, we have systematic risk and nonsystematic risk, which are
additive:
Total risk = General risk + Specific risk
= Market risk + Issuer risk
= Systematic risk + Nonsystematic risk
Systematic (Market) Risk:
Risk attributable to broad macro factors affecting all securities
Systematic Risk is an investor can construct a diversified portfolio and eliminate pan of the
total risk, the diversifiable or non-market part. What is left is the non-diversifiable portion
or the market risk. Variability in a security's total returns that is directly associated with
overall movements in the general market or economy is called systematic (market) risk.
Virtually all securities have some systematic risk, whether bonds or stocks, because
systematic risk directly encompasses the interest rate, market, and inflation risks. The
investor cannot escape this part of the risk, because no matter how well he or she
diversifies, the risk of the overall market cannot be avoided. If the stock market declines
sharply, most stocks will be adversely affected; if it rises strongly, as in the last few months
of 1982, most stocks will appreciate in value. These movements occur regardless of what
any single investor does. Clearly, market risk is critical to all investors.
Nonsystematic (Non-market) Risk:
Risk attributable to factors unique to the security
Nonsystematic Risk is the variability in a security's total returns not related to overall
market variability is called the nonsystematic (non-market) risk. This risk 1s unique to a
particular security and is associated with such factors as business and financial risk as well
as liquidity risk. Although all securities tend to have some nonsystematic risk, it is generally
connected with common stocks.
MEASURING RETURNS:
1. Total Return:
Percentage measure relating all cash flows on a security for a given time period 10 its
purchase price
A correct returns measure must incorporate the two components of return, yield and price
change, as discussed earlier. Returns across time or from different securities can be
measured and compared using the total return concept. Formally, the total return (TR) for a
given holding period is a decimal (or percentage) number relating all the cash flows
received by an investor during any designated time period to the purchase price of the
asset. Total return is defined as:
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TR = Any cash payments received + Price changes over the period
Price at which the asset is purchased
The dollar price change over the period, defined as the difference between the beginning (or
purchase) price and, the ending (or sale) price, can be either positive (sales price exceeds
purchase price), negative (purchase price exceeds sales price), or zero. The cash payments
can be either positive or zero. Netting the two items in the numerator together and dividing
by the purchase price results in a decimal return figure that can easily be converted into
percentage form. Note that in using the TR, the two components of return, yield and price
change, have been measured.
The general equation for calculating TR is;
TR = CFt + (PE - PB)
PB
= CFt + PC
PB
Where;
CFt = cash flows during the measurement period t
PE = price at the end of period t or sale price
PB = purchase price of the asset or price at the beginning of the period
PC = change in price during the period, or PE minus PB
The cash flow for bond pomes from the interest payments received, and that for a stock
comes from the dividends received. For some assets, such as a warrant or a stock that pays
no dividends, there is only a price change.
2. Return Relative:
It is often necessary to measure returns on a slightly different basis than TRs. This is
particularly true when calculating either a cumulative wealth index or a geometric mean,
both of which are explained below, because negative returns cannot be used in the
calculation. The return relative (RR) solves this problem by adding 1.0 to the total return.
RR = TR in decimal form + 1.0
TR in decimal form = RR - 1.0
Although return relatives may be less than 1.0, they will be greater than zero, thereby
eliminating negative numbers.
3. Cumulative Wealth Index:
Cumulative wealth over time given an initial wealth and a series of returns on some asset
Return measures such as TRs measure changes in the level of wealth. At times, however, it
is more desirable to measure levels of wealth {or prices) rather than changes. In other
words, we measure the cumulative effect of returns over time given some stated beginning
dollar amount invested, which typically is shown as $1 for convenience. Having calculated
ending wealth (cumulative wealth) over some period on the base of a beginning $1, it is
simple enough to multiply by the actual beginning amount, such as $10,000 or $100,000 or
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whatever the number is. The value of the cumulative wealth index, CWIn is computed, as:
CWIn = WI0 (1 + TR1) (1 + TR2) ... (1 + TRn)
Where;
CWIB = the cumulative wealth index as of the end of period n
WI0  = the beginning index value, typically $1
TR1, n = the periodic TRs in decimal form
Taking a Global Perspective:
International investing offers potential return opportunities and potential reduction in risk
through diversification. Based on the historical record, investments in certain foreign
markets would have increased investor returns during certain periods-of time. However,
investors need to understand how these-returns are calculated and the risk they are taking.
International Returns and Currency Risk:
When investors buy and sell assets in other countries, they must consider exchange rate
risk or currency risk. This risk can convert a gain from an investment into .a loss or a loss
from an investment into a gain. We need to remember that international stocks are priced
in local currencies, for example, a Swiss stock is priced in Swiss francs and a Japanese
stock is priced in yen. For a U.S. investor, the ultimate return to him or her in spendable
dollars depends upon the rate of exchange between the foreign currency and the dollar, and
this rate typically changes daily. Currency risk is the risk that the changes in the value of the
dollar and the foreign currency involved will be unfavorable; however, like risk in general,
currency risk can work to the investor's favor, enhancing the return that would otherwise be
received.
An investment denominated in an appreciating currency relative to the investor's domestic
currency will experience a gain from the currency movement whereas an investment
denominated in a depreciating currency relative to the investor's domestic currency will
experience a decrease in the return because of the currency movement. Said differently,
when you buy a foreign asset, you are selling the dollar, and when you cash in by selling the
asset, you are buying back the dollar.
Total return in = RR x Ending value of foreign currency
Domestic terms
Beginning value of foreign currency
SUMMARY STATISTICS FOR RETURNS:
The total return, return relative, and wealth index are useful measures of return for a
specified period of time. Also needed in investment analysis are statistics to describe a
series of returns. "For example, investing in a particular stock for 10 years or a different
stock in each of 10 years could result in 10 TRs, which must be described by one or more
statistics. Two such measures used with returns data are described below.
Arithmetic Mean the best known statistic to most people is the arithmetic mean. Therefore,
when someone refers to the mean return they usually are referring to the arithmetic mean
unless otherwise specified. The arithmetic mean, customarily designated by the symbol;
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X(X-bar), of a set of values is calculated as:
X=X
n
or the sum of each of the values being considered divided by the total, number of values n.
Geometric Mean the arithmetic mean return is an appropriate measure of the central
tendency of a distribution consisting of returns calculated for a particular time" period, such
as 10 years. However, when percentage changes in value over time are involved, as a result
of compounding, the arithmetic mean of these changes can be misleading. A different mean,
the geometric mean, is needed to describe accurately the "true" average rate of return, over
multiple periods.
The geometric mean return measures the compound rate of growth over time. It is often
used in investments and finance to reflect the steady growth rate of invested funds over
some past period; that is, the uniform rate at which money actually few over time per
period. Therefore, it allows us to measure the realized change in wealth over multiple
periods.
.
The geometric mean is defined as the nth root of the product resulting from multiplying a
series of return relatives together,
G = [(1 + TR1) (1 + TR2)... (1 + TRn)]1/n - 1
where TR is a series of total returns in decimal form. Note that adding 1.0 to each total
return produces a return relative. Return relatives are used in calculating geometric mean
returns, because TRs, which can be negative, cannot be used.
Arithmetic Mean versus Geometric Mean:
When should we use the arithmetic mean and when should we use the geometric mean to
describe the returns from financial assets? The answer depends on the investor's objective:
The arithmetic mean is a better measure of average (typical) performance over single
periods. It is the best estimate of the expected return for next period.
The geometric mean is a better measure of the change in wealth over the past (multiple
periods). It is a backward-looking concept, measuring the realized compound rate of return
at which money grew- over a specified period.
Inflation Adjusted Returns:
All of the returns discussed above art nominal returns, or money returns. They measure
dollar amounts or changes but say nothing about the purchasing power of these dollars. To
capture this dimension, we need to consider real returns, or inflation-adjusted returns. To
calculate inflation-adjusted returns, we divide 1 + nominal total return by 1 + the inflation
rate, this calculation is sometimes simplified by subtracting rather than dividing, producing
a close approximation.
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Investment Analysis & Portfolio Management (FIN630)
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TRIA = (1 + TR) - 1
(1 + IF)
Where;
TRIA = the inflation-adjusted total return
IF
= the rate of inflation
This equation applies to both individual years and average total returns.
Risk Premiums:
A risk premium is the additional return investors expect to receive, or did receive, by taking
on increasing amounts of risk. It measures the payoff for taking various types of risk. Such
premiums can be calculated between any two classes of securities.
An often-discussed risk premium is the equity risk premium, defined as the difference
between the return on stocks and a risk-free rate (proxied by the return on Treasury bills).
The equity risk premium measures the additional compensation for assuming risk, since
Treasury bills have no practical risk (on a nominal basis). Obviously, common stock
investors care whether the expected risk premium is 5 percent, or 8 percent, because that
affects what they earn on their investment in stocks. Holding interest rates constant, a
narrowing of the equity risk premium implies a decline in the rate of return on steaks,
because the amount carried beyond the risk-free rate is reduced.
MORE ON THE RELATIONSHIP BETWEEN RISK AND RETURN:
Risk and potential return need to be analyzed together throughout the investment decision-
making process. Considering their relationship is a big part of what investment advisers get
paid to do.
The Direct Relationship:
The fundamental relationship between risk and return is well known to those who
have studied the market.
The more risk someone bears, the higher are their expected return. It also points out that
some rate of return can be earned without bearing any risk, and is called the riskless rate of
interest, or the risk free rate in finance theory. Two important points should be noted. First,
the risk-return relationship is based on expected return. Expected return is a before the fact,
not after the fact concept. It is not correct to say that riskier securities have higher returns,
although people often make this statement. If riskier securities always had a higher return
they would not be risky. Sometimes an investor is hurt by a risk taken that resulted in a
negative return. Such is the essence of risk.
The second important point is that the risk we are talking about is unavoidable, or
undiversifiable, risk. An investor is not generally rewarded for bearing risk that could have
been diversified away.
Empirical financial research reveals clear evidence of the direct relationship between
systematic risk and expected return. Riskier portfolios, on average, earn higher.
Additionally, returns on well diversified portfolios tend to plot in a generally linear fashion.
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The point of this discussion is that whether looking ahead to possible future returns or
looking back at realized results, a person can usually observe this direct relationship
between risk and return. Once again, though, it is not accurate to conclude that "higher risk
means higher return." Risky investments often lose money for their owners over the short
run. They may also earn less than "safer" investments.
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