Investment Analysis
CH1
Measures of historical rates of return
The period during which you own an investment is called its holding period, and the return for
that period is the holding period return (HPR).
HPR = En ding valueinvest m ent /beginning valueinvest m ent
The HPR will always be zero or greater.
Although the HPR helps us express the change in value of an investment, investors generally
evaluate returns in percentage terms on an annual basis, referred to as the
holding period yield.
HPY = HPR − 1
Mean historical returns
Given a set of annual rates of returns (HPYs) for an individual investment, there are two summa-
ry measures of return performance.
Arithmetic mean (AM) =
Geometric mean (GM) =
The AM is best used as an expected value for an individual year, while the GM is the best mea-
sure of long-term performance since it measures the compound annual rate of return for the
asset being measured.
Calculating expected rates of return
Risk is the uncertainty that an investment will earn its expected rate of return. The expected
return from an investment is defined as:
E(R)=
Where P is the probability and R the possible return.
,Investment Analysis
Measuring the risk of the expected rates of return
Two possible measures of risk have received support on portfolio theory: the variance and the
standard deviation of the estimated distribution of expected returns.
The larger the variance for an expected rate of return, the greater
the dispersion of the expected returns and the greater the risk of the investment.
A relative measure of risk
If there are major differences in the expected rates if return - it is necessary to use a measure of
relative variability to indicate risk per unit of expected return.
Risk measures for historical returns
To measure the risk for a series of historical rates of returns, we use the same measures as for
expected returns except that we consider the historical holding period yields as follows:
The real risk free rate
The real risk-free rate is the basic interest rate, assuming no inflation and no uncertainty about
future flows. This RRFR of internet is the price charged for the risk-free exchange between cur-
rent goods and future goods.
The subjective factor is the time preference of individuals for the consumption of income.
, Investment Analysis
The objective factor that influences the RRFR is the set of investment opportunities available
in the economy.
The nominal rate of interest on a default free investment is not stable in the long run or short
run, even though the underlying determinants of the RRFR are quite stable.
Two factors that influence the nominal risk free rate: (1) the tightness in the capital markets, (2)
the expected rate of inflation.
An investors nominal required rate of return on a risk-free investment should be:
Risk premium
The increase in the required rate of return over the NRFR is the risk premium (RP).
Business risk is the uncertainty of income flows caused by the nature of a firm’s busi-
ness.
Financial risk is the uncertainty introduced by the method by which the firm finances its
investments.
Liquidity risk is the uncertainty introduced by the secondary market for an investment.
The investor expects to be able to convert the security into cash and use the proceeds
for current consumption or other investments. The more difficult it is to make this con-
version to cash, the greater the liquidity risk.
Exchange rate risk is the uncertainty of returns to an investor who acquires securities
denominated in a currency different from his or her own.
Country risk (political risk) is the uncertainty caused by the possibility of major change
in the political or economic environment of a country.
The discussion of risk components can be considered a security’s fundamental risk because it
deals with intrinsic factors that should affect a security’s volatility of returns over time.
Systematic risk, the portion of an individual asset’s total variance that is attributable to the
variability of the total market portfolio. The risk premium for an individual earning asset is a
function of the asset’s systematic risk with the aggregate market portfolio of risky assets. The
measure of an asset’s systematic risk is referred to as its beta.
Relationship between risk and return
The security market line (SML) reflects the combination of risk and return available on alterna-
tive investments. It reflects the risk-return combinations available for all risky assets in the capi-
tal market at a given time.
Three things can happen with the SML:
CH1
Measures of historical rates of return
The period during which you own an investment is called its holding period, and the return for
that period is the holding period return (HPR).
HPR = En ding valueinvest m ent /beginning valueinvest m ent
The HPR will always be zero or greater.
Although the HPR helps us express the change in value of an investment, investors generally
evaluate returns in percentage terms on an annual basis, referred to as the
holding period yield.
HPY = HPR − 1
Mean historical returns
Given a set of annual rates of returns (HPYs) for an individual investment, there are two summa-
ry measures of return performance.
Arithmetic mean (AM) =
Geometric mean (GM) =
The AM is best used as an expected value for an individual year, while the GM is the best mea-
sure of long-term performance since it measures the compound annual rate of return for the
asset being measured.
Calculating expected rates of return
Risk is the uncertainty that an investment will earn its expected rate of return. The expected
return from an investment is defined as:
E(R)=
Where P is the probability and R the possible return.
,Investment Analysis
Measuring the risk of the expected rates of return
Two possible measures of risk have received support on portfolio theory: the variance and the
standard deviation of the estimated distribution of expected returns.
The larger the variance for an expected rate of return, the greater
the dispersion of the expected returns and the greater the risk of the investment.
A relative measure of risk
If there are major differences in the expected rates if return - it is necessary to use a measure of
relative variability to indicate risk per unit of expected return.
Risk measures for historical returns
To measure the risk for a series of historical rates of returns, we use the same measures as for
expected returns except that we consider the historical holding period yields as follows:
The real risk free rate
The real risk-free rate is the basic interest rate, assuming no inflation and no uncertainty about
future flows. This RRFR of internet is the price charged for the risk-free exchange between cur-
rent goods and future goods.
The subjective factor is the time preference of individuals for the consumption of income.
, Investment Analysis
The objective factor that influences the RRFR is the set of investment opportunities available
in the economy.
The nominal rate of interest on a default free investment is not stable in the long run or short
run, even though the underlying determinants of the RRFR are quite stable.
Two factors that influence the nominal risk free rate: (1) the tightness in the capital markets, (2)
the expected rate of inflation.
An investors nominal required rate of return on a risk-free investment should be:
Risk premium
The increase in the required rate of return over the NRFR is the risk premium (RP).
Business risk is the uncertainty of income flows caused by the nature of a firm’s busi-
ness.
Financial risk is the uncertainty introduced by the method by which the firm finances its
investments.
Liquidity risk is the uncertainty introduced by the secondary market for an investment.
The investor expects to be able to convert the security into cash and use the proceeds
for current consumption or other investments. The more difficult it is to make this con-
version to cash, the greater the liquidity risk.
Exchange rate risk is the uncertainty of returns to an investor who acquires securities
denominated in a currency different from his or her own.
Country risk (political risk) is the uncertainty caused by the possibility of major change
in the political or economic environment of a country.
The discussion of risk components can be considered a security’s fundamental risk because it
deals with intrinsic factors that should affect a security’s volatility of returns over time.
Systematic risk, the portion of an individual asset’s total variance that is attributable to the
variability of the total market portfolio. The risk premium for an individual earning asset is a
function of the asset’s systematic risk with the aggregate market portfolio of risky assets. The
measure of an asset’s systematic risk is referred to as its beta.
Relationship between risk and return
The security market line (SML) reflects the combination of risk and return available on alterna-
tive investments. It reflects the risk-return combinations available for all risky assets in the capi-
tal market at a given time.
Three things can happen with the SML:
