The Investment Process and Rate of Return

 
An overview of the investment
process
 
Why investors invest?
 
By saving instead of spending,
Individuals trade-off
Present consumption
For a larger future consumption
 
How Do We Measure The Rate Of
Return On An Investment ?
 
The 
pure rate of interest
 is the
exchange rate between future
consumption and present
consumption.  Market forces
determine this rate.
 
 
People’s willingness to pay the
difference for borrowing today and
their desire to receive a surplus on
their savings give rise to an interest
rate referred to as the 
pure time
value of money
.
 
How Do We Measure The Rate Of
Return On An Investment ?
 
 
If the future payment will be
diminished in value because of
inflation
, then the investor will
demand an interest rate higher than
the pure time value of money to 
also
cover the expected inflation
 expense.
 
How Do We Measure The Rate Of
Return On An Investment ?
 
 
If the future payment from the
investment is not certain
, the
investor will demand an interest
rate that exceeds the pure time
value of money plus the inflation
rate to 
provide a risk premium
 to
cover the investment risk.
 
How Do We Measure The Rate Of
Return On An Investment ?
Defining an Investment
 
 
A current commitment of $ for a
period of time in order to derive
future payments that will
compensate for:
the time the funds are committed
the expected rate of inflation
uncertainty of future flow of funds.
Measures of
    Historical Rates of Return
Holding Period Return
Measures of
    Historical Rates of Return
 
Holding Period Yield
HPY = HPR - 1
1.10 - 1 = 0.10 = 10%
1.2
 
Annual Holding Period Return
Annual HPR = HPR 
1/n
where n = number of years investment is held
Annual Holding Period Yield
Annual HPY = Annual HPR - 1
 
Measures of
    Historical Rates of Return
Measures of
    Historical Rates of Return
 
Arithmetic Mean
1.4
Measures of
    Historical Rates of Return
 
Geometric Mean
1.5
 
A Portfolio of Investments
 
 
The mean historical rate of return for
a portfolio of investments is
measured as the weighted average
of the HPYs for the individual
investments in the portfolio.
Computation of Holding
Period Yield for a Portfolio
Expected Rates of Return
 
Risk is uncertainty that an
investment will earn its expected
rate of return
Probability is the likelihood of an
outcome
Expected Rates of Return
1.6
 
Risk Aversion
 
 
The assumption that most investors
will choose the least risky
alternative, all else being equal and
that they will not accept additional
risk unless they are compensated in
the form of higher return
 
Measuring the Risk of
Expected Rates of Return
 
1.7
 
Measuring the Risk of
Expected Rates of Return
 
Standard Deviation is the square
root of the variance
 
1.8
Measuring the Risk of
Expected Rates of Return
 
 
Coefficient of variation (CV) 
a measure of
relative variability that indicates risk per unit
of return
  
     
Standard Deviation of Returns
Expected Rate of Returns
1.9
 
Measuring the Risk of
Historical Rates of Return
 
variance of the series
holding period yield during period i
expected value of the HPY that is equal
to the arithmetic mean of the series
the number of observations
 
1.10
Determinants of
Required Rates of Return
 
Time value of money
Expected rate of inflation
Risk involved
The Real Risk Free Rate (RRFR)
 
 
Assumes no inflation.
Assumes no uncertainty about
future cash flows.
Influenced by time preference for
consumption of income and
investment opportunities in the
economy
 
Adjusting For Inflation
 
Real RFR =
 
1.12
Nominal Risk-Free Rate
 
 
Dependent upon
Conditions in the Capital Markets
Expected Rate of Inflation
 
Adjusting For Inflation
 
Nominal RFR =
(1+Real RFR) x (1+Expected Rate of Inflation) - 1
 
1.11
Facets of Fundamental Risk
 
Business risk
Financial risk
Liquidity risk
Exchange rate risk
Country risk
Business Risk
 
Uncertainty of income flows caused by
the nature of a firm’s business
Sales volatility and operating leverage
determine the level of business risk
.
Financial Risk
 
Uncertainty caused by the use of debt
financing
.
Borrowing requires fixed payments which
must be paid ahead of payments to
stockholders.
The use of debt increases uncertainty of
stockholder income and causes an increase
in the stock’s risk premium.
Liquidity Risk
 
Uncertainty is introduced by the secondary
market for an investment.
How long will it take to convert an investment
into cash?
How certain is the price that will be received?
Exchange Rate Risk
 
Uncertainty of return is 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.
Country Risk
 
Political risk is 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
 
Risk Premium
 
f 
(Business Risk, Financial Risk,
Liquidity Risk, Exchange Rate Risk,
Country Risk)
or
f 
(Systematic Market Risk)
Risk Premium
and Portfolio Theory
 
The relevant risk measure for an
individual asset is its co-movement
with the market portfolio
Systematic risk relates the variance of
the investment to the variance of the
market
Beta measures this systematic risk of
an asset
 
Fundamental Risk
versus Systematic Risk
 
Fundamental risk comprises business
 
risk, financial risk, liquidity risk, exchange
rate risk, and country risk
Systematic risk refers to the portion of an
individual asset’s total variance attributable
to the variability of the total market
portfolio
 
Relationship Between
Risk and Return
 
Exhibit 1.7
 
Changes in the Required Rate of Return
Due to Movements Along the SML
 
Exhibit 1.8
 
Changes in the Slope of the SML
 
RP
i
 = E(R
i)
 - NRFR
  
where:
RP
i
 = risk premium for asset 
i
E(R
i)
  = the expected return for asset
 i
NRFR = the nominal return on a risk-free asset
 
Market Portfolio Risk
 
 
The market risk premium for the market
portfolio (contains all the risky assets in the
market) can be computed:
RP
m
 = E(R
m
)- NRFR where:
RP
m
 = risk premium on the market portfolio
E(R
m
) = 
expected return on the market portfolio
NRFR = expected return on a risk-free asset
 
     
Change in
Market Risk Premium
 
Capital Market Conditions,
Expected Inflation, and the SML
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Investors choose to invest by saving instead of spending to trade off present consumption for larger future consumption. The rate of return on an investment is measured by factors such as the pure rate of interest, time value of money, inflation impact, and risk premium. Investments involve committing funds for future returns that compensate for factors like inflation and uncertainty. Historical rates of return can be evaluated through measures like the Holding Period Return.

  • Investment Process
  • Rate of Return
  • Saving
  • Future Consumption
  • Time Value of Money

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  1. An overview of the investment process

  2. Why investors invest? By saving instead of spending, Individuals trade-off Present consumption For a larger future consumption

  3. How Do We Measure The Rate Of Return On An Investment ? The pure rate of interest is the exchange rate between future consumption and present consumption. Market forces determine this rate. + = . 1 00 4 % . 1 04 SR SR

  4. How Do We Measure The Rate Of Return On An Investment ? People s willingness to pay the difference for borrowing today and their desire to receive a surplus on their savings give rise to an interest rate referred to as the pure time value of money.

  5. How Do We Measure The Rate Of Return On An Investment ? If the future payment will be diminished in value because of inflation, then the investor will demand an interest rate higher than the pure time value of money to also cover the expected inflation expense.

  6. How Do We Measure The Rate Of Return On An Investment ? If the future payment from the investment is not certain, the investor will demand an interest rate that exceeds the pure time value of money plus the inflation rate to provide a risk premium to cover the investment risk.

  7. Defining an Investment A current commitment of $ for a period of time in order to derive future payments that will compensate for: the time the funds are committed the expected rate of inflation uncertainty of future flow of funds.

  8. Measures of Historical Rates of Return Holding Period Return Ending Value of Investment = HPR Beginning Value of Investment SR220 = . 1 = 10 SR200

  9. Measures of Historical Rates of Return Holding Period Yield HPY = HPR - 1 1.10 - 1 = 0.10 = 10% 1.2

  10. Measures of Historical Rates of Return Annual Holding Period Return Annual HPR = HPR 1/n where n = number of years investment is held Annual Holding Period Yield Annual HPY = Annual HPR - 1

  11. Measures of Historical Rates of Return 1.4 Arithmetic Mean = AM HPY/ n where : the = HPY sum of annual holding period yields

  12. Measures of Historical Rates of Return 1.5 Geometric Mean 1 = GM HPR 1 n where : product the = of annual the holding period returns follows as : ( ) ( ) ( ... ) HPR HPR HPR 1 2 n

  13. A Portfolio of Investments The mean historical rate of return for a portfolio of measured as the weighted average of the HPYs for the individual investments in the portfolio. investments is

  14. Computation of Holding Period Yield for a Portfolio # Begin Price $ $ $ Beginning Mkt. Value 1,000,000 $ 4,000,000 $ 15,000,000 $ 20,000,000 $ Ending Price 12 $ 21 $ 33 $ Ending Mkt. Value 1,200,000 $ 4,200,000 $ 16,500,000 $ 21,900,000 $ Market Wt. 0.05 0.20 0.75 Wtd. HPY 0.010 0.010 0.075 0.095 Stock A B C Total Shares 100,000 200,000 500,000 HPR HPY 1.20 20% 1.05 1.10 10% 10 20 30 5% 21,900,000 $ 20,000,000 $ HPR = = 1.095 HPY = 1.095 - 1 = 0.095 = 9.5%

  15. Expected Rates of Return Risk is uncertainty that an investment will earn its expected rate of return Probability is the likelihood of an outcome

  16. Expected Rates of Return 1.6 = Expected Return E(R ) i n = i 1 ( Probabilit y of Return) (Possible Return) + + + [(P i = )(R ) (P )(R ) .... (P R ) 1 1 )(R 2 2 n n n P ( ) i i 1

  17. Risk Aversion The assumption that most investors will choose the alternative, all else being equal and that they will not accept additional risk unless they are compensated in the form of higher return least risky

  18. Measuring the Risk of Expected Rates of Return 1.7 = Variance ( ) n = n 2 Probabilit ( y) (Possible Return - Expected Return) i 1 = i 2 P ( )[R E(R )] i i i 1

  19. Measuring the Risk of Expected Rates of Return 1.8 Standard Deviation is the square root of the variance

  20. Measuring the Risk of Expected Rates of Return 1.9 Coefficient of variation (CV) a measure of relative variability that indicates risk per unit of return Standard Deviation of Returns Expected Rate of Returns i = E(R)

  21. Measuring the Risk of Historical Rates of Return n 2 HPY [ = = HPY i 1.10 = 2/n E ( HPY) i i 1 2 variance of the series holding period yield during period i expected value of the HPY that is equal to the arithmetic mean of the series the number of observations = = E(HPY) = n

  22. Determinants of Required Rates of Return Time value of money Expected rate of inflation Risk involved

  23. The Real Risk Free Rate (RRFR) Assumes no inflation. Assumes no uncertainty about future cash flows. Influenced by time preference for consumption of income and investment opportunities in the economy

  24. Adjusting For Inflation 1.12 Real RFR = + 1 ( Nominal RFR) 1 + (1 Rate of Inflation)

  25. Nominal Risk-Free Rate Dependent upon Conditions in the Capital Markets Expected Rate of Inflation

  26. Adjusting For Inflation 1.11 Nominal RFR = (1+Real RFR) x (1+Expected Rate of Inflation) - 1

  27. Facets of Fundamental Risk Business risk Financial risk Liquidity risk Exchange rate risk Country risk

  28. Business Risk Uncertainty of income flows caused by the nature of a firm s business Sales volatility and operating leverage determine the level of business risk.

  29. Financial Risk Uncertainty caused by the use of debt financing. Borrowing requires fixed payments which must be paid ahead of payments to stockholders. The use of debt increases uncertainty of stockholder income and causes an increase in the stock s risk premium.

  30. Liquidity Risk Uncertainty is introduced by the secondary market for an investment. How long will it take to convert an investment into cash? How certain is the price that will be received?

  31. Exchange Rate Risk Uncertainty of return is 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.

  32. Country Risk Political risk is 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

  33. Risk Premium f (Business Risk, Financial Risk, Liquidity Risk, Exchange Rate Risk, Country Risk) or f (Systematic Market Risk)

  34. Risk Premium and Portfolio Theory The relevant risk measure for an individual asset is its co-movement with the market portfolio Systematic risk relates the variance of the investment to the variance of the market Beta measures this systematic risk of an asset

  35. Fundamental Risk versus Systematic Risk Fundamental risk comprises business risk, financial risk, liquidity risk, exchange rate risk, and country risk Systematic risk refers to the portion of an individual asset s total variance attributable to the variability of the total market portfolio

  36. Relationship Between Risk and Return Exhibit 1.7 Rateof Return Low Risk (Expected) Security Market Line Average Risk High Risk The slope indicates the required return per unit of risk RFR Risk (business risk, etc., or systematic risk-beta)

  37. Changes in the Required Rate of Return Due to Movements Along the SML Expected Exhibit 1.8 Rate Security Market Line Movements along the curve that reflect changes in the risk of the asset RFR Risk (business risk, etc., or systematic risk-beta)

  38. Changes in the Slope of the SML RPi = E(Ri) - NRFR RPi = risk premium for asset i E(Ri) = the expected return for asset i NRFR = the nominal return on a risk-free asset where:

  39. Market Portfolio Risk The market risk premium for the market portfolio (contains all the risky assets in the market) can be computed: RPm = E(Rm)- NRFR where: RPm = risk premium on the market portfolio E(Rm) = expected return on the market portfolio NRFR = expected return on a risk-free asset

  40. Change in Market Risk Premium Expected Return E(R) New SML Rm' Original SML Rm RFR Risk

  41. Capital Market Conditions, Expected Inflation, and the SML Expected Return Rate of Return New SML Original SML RFR' RFR Risk

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