- Any investment requires committing funds for a period of time in order to receive future payments that compensate for the time value of money, expected inflation, and investment risk. - There are different ways to calculate rates of return over multiple periods, including equivalent annual return, arithmetic mean, and geometric mean. - Risk is the uncertainty of an investment's expected return, which is influenced by factors like business risk, financial risk, liquidity risk, exchange rate risk, and country risk. Investors require higher returns to compensate for higher risk.

3. o
o
o
o
Any investment involves a current commitment of
funds for some period of time in order to derive
future payments that will compensate for:
the time the funds are committed (the real rate of
return)
the expected rate of inflation (inflation premium)
uncertainty of future flow of funds (risk premium)

5. o
o
EAR
1 HPR
1
N
1
o
EAR = Equivalent
Annual Return
HPR = Holding Period
Return
N = Number of years

6. AM = Arithmetic Mean
AM
R1 R2 ... RN
N
GM = Geometric Mean
Ri = Annual HPRs
N = Number of years
GM
1 R1 1 R2 ... 1 RN
1
N
1

7. o
The mean historical rate of return for a
portfolio of investments is measured as
the weighted average of the HPRs for
the individual investments in the
portfolio, or the overall change in the
value of the original portfolio

8. o
o
Risk is the uncertainty whether an
investment will earn its expected rate of
return
Probability is the likelihood of an outcome
n
E(R i )
(Probabilit y of Return)
i 1
n
(Pi )(R i )
i 1
(Possible Return)

10. o
o
Much of modern finance is based on the
principle that investors are risk averse
Risk aversion refers to the assumption that,
all else being equal, most investors will
choose the least risky alternative and that
they will not accept additional risk unless
they are compensated in the form of higher
return

11. n
HPR i
2
E HPRi
i 1
N
2
Where:
= Variance (of the pop)
HPR = Holding Period Return i
E(HPR)i = Expected HPR*
N = Number of years

12. n
2
(Pi ) R i E(R)
2
i 1
= Variance
Note: Because we multiply by the
probability of each return occurring,
we do NOT divide by N. If each
probability is the same for all returns,
then the variance can be calculated by
either multiplying by the probability or
dividing by N.
Ri = Return in period i
E(R) = Expected Return
Pi = Probability of Ri occurring

13. n
Pi [R i -E(R i )]2
i 1
n
Pi [R i -E(R i )]2
i 1
1
2
Standard Deviation is a measure of
dispersion around the mean. The higher
the standard deviation, the greater the
dispersion of returns around the mean and
the greater the risk.

14. o
o
Coefficient of variation (CV) is a measure
of relative variability
CV indicates risk per unit of return, thus
making comparisons easier among
investments with large differences in mean
returns

16. o
Three factors influence an
investor’s required rate of return
oReal rate of return
oExpected rate of inflation during the
period
oRisk

17. oAssumes no inflation.
oAssumes no uncertainty about future
cash flows.
oInfluenced by the time preference for
consumption of income and
investment opportunities in the
economy

18. 1 Nominal
1 Real 1 Expected Inflation
The nominal risk free rate of return is
dependent upon:
Conditions in the Capital Markets
Expected Rate of Inflation

19. o
Five factors affect the standard
deviation of returns over time.
oBusiness risk:
oFinancial risk
oLiquidity risk
oExchange rate risk
oCountry risk

20. oUncertainty of income flows caused by the
nature of a firm’s business
oSales volatility and operating leverage
determine the level of business risk.
o Uncertainty caused by the use of debt financing.
o Borrowing requires fixed payments which must
be paid ahead of payments to stockholders.
o The use of debt increases uncertainty of
stockholder income and causes an increase in the
stock’s risk premium.

21. o
the uncertainty introduced by the secondary market
for an investment.
o How long will it take to convert an investment into cash?
o How certain is the price that will be received?
o
o
the uncertainty introduced by acquiring securities
denominated in a currency different from that of the
investor.
Changes in exchange rates affect the investors return
when converting an investment back into the
“home” currency.

22. o
o
Country risk (also called political risk) refers to the
uncertainty of returns caused by the possibility of a
major change in the political or economic
environment in a country.
Individuals who invest in countries that have
unstable political-economic systems must include a
country risk-premium when determining their
required rate of return

25. Frank K. Reilly & Keith C. Brown
REFERENCE