INVESTMENT MANAGEMENT 314
Chapter 1: Investment Setting
What is an investment?
• Investment
- What you do with savings to make them increase over time
• Reason for saving
- Trade-off of present consumption for a higher level of future consumption
• Inflation
- If investors expect a change in prices, they will require a higher rate of return to compensate for
it
• Uncertainty
- If the future payment from the investment is not certain, the investor will demand an interest
rate that exceeds the nominal risk-free interest rate
o Investment risk
o Risk premium
Investment defined
• Investment
- The current commitment of dollars for a period of time in order to derive future payments that
will compensate the investor for:
o The time the funds are committed
o The expected rate of inflation during this time period
o The uncertainty of the future payments
• The “investor”
- Individual
- Government
- Pension funds
- Corporation etc.
• Investment examples
- Corporations in plant and equipment
- Individuals in stocks, bons, commodities, or real estate etc.
Measures of Risk and Return:
• Historical rate of return on an individual investment over its holding period
• Average historical rate of return for an individual investment over a number of time periods
• Average rate of return for a portfolio of investments
• Traditional measures of risk
- Variance and standard deviation
• Expected rate of return for an investment
Measures of Historical rates of return:
• Holding Period Return (HPR)
• Holding Period Yield (HPY)
, • Annual HPR and HPY
• Example 1:
- Assume that you invested $1690 in March 2020 and get back $3000 at mid-march 2021. What
are the HPR and the HPY for your investment in Amazon?
• Example 2:
- Your investment of $40 in Apple Stock is worth $120 in two years while the investment of $400
in Netflix Stock is worth $580 in six months. What are the annual HPRs and the HPYs on these
two stocks?
Mean Historical rates of return
• Suppose you have a set of annual rates of return (HPYs or HPRs) for an investment.
• How do you measure the mean annual return?
- Arithmetic Mean Return (AM)
- Geometric Mean Return (GM)
• Example 3
- Suppose you invested $100 three years ago and it is worth $110.40 today. The information
below shows the annual ending values and HPR and HPY. This example illustrates the
computation of the AM and the GM over a three-year period for an investment.
,AM = [(0.15) + (0.20) + (-0.20)]/3
= 0.15/3
= 5%
GM = [(1.15) + (0.20) + (-0.20)]1/3 – 1
= (1.104)1/3 – 1
= 1.03333 – 1
= 3.35%
Comparison of AM and GM
• When rates of return of the same for all years, the AM and the GM will be equal.
• When rates of return are not the same for all years, the AM will always be higher than the GM
• While the AM is best used as an “expected value” for an individual year, while the GM is the best
measure of an assets long-term performance.
A Portfolio of investments
• The mean historical rate of return (HPY) for a portfolio of investments is measured as the weighted
average of the HPYs for the individual investments in the portfolio, or the overall percentage
change in value of the original portfolio
• The weights used in computing the averages are the relative beginning market values for each
investment
• This is referred to as dollar-weighted or value-weighted mean rate of return
Exhibit 1.1
• Market weight are based on beginning vales → Beginning market value/total beginning market
value = market weight
Calculating Expected Rates of Return
• Risk is the uncertainty of the future outcomes of an investment
, - There are many possible returns or outcomes from an investment due to the uncertainty
- Probability is the likelihood of an outcome
- The sum of the probabilities of all the possible outcomes is equal to 1.0
• The expected return from an investment is defined as:
Measuring risk
• Statistical measures allow comparison of the return and risk measures for alternative investments
directly
• Two possible measures of risk (uncertainty) have received support in theoretical work on portfolio
theory:
- Variance
- Standard deviation of the estimated distribution of expected returns
Chapter 1: Investment Setting
What is an investment?
• Investment
- What you do with savings to make them increase over time
• Reason for saving
- Trade-off of present consumption for a higher level of future consumption
• Inflation
- If investors expect a change in prices, they will require a higher rate of return to compensate for
it
• Uncertainty
- If the future payment from the investment is not certain, the investor will demand an interest
rate that exceeds the nominal risk-free interest rate
o Investment risk
o Risk premium
Investment defined
• Investment
- The current commitment of dollars for a period of time in order to derive future payments that
will compensate the investor for:
o The time the funds are committed
o The expected rate of inflation during this time period
o The uncertainty of the future payments
• The “investor”
- Individual
- Government
- Pension funds
- Corporation etc.
• Investment examples
- Corporations in plant and equipment
- Individuals in stocks, bons, commodities, or real estate etc.
Measures of Risk and Return:
• Historical rate of return on an individual investment over its holding period
• Average historical rate of return for an individual investment over a number of time periods
• Average rate of return for a portfolio of investments
• Traditional measures of risk
- Variance and standard deviation
• Expected rate of return for an investment
Measures of Historical rates of return:
• Holding Period Return (HPR)
• Holding Period Yield (HPY)
, • Annual HPR and HPY
• Example 1:
- Assume that you invested $1690 in March 2020 and get back $3000 at mid-march 2021. What
are the HPR and the HPY for your investment in Amazon?
• Example 2:
- Your investment of $40 in Apple Stock is worth $120 in two years while the investment of $400
in Netflix Stock is worth $580 in six months. What are the annual HPRs and the HPYs on these
two stocks?
Mean Historical rates of return
• Suppose you have a set of annual rates of return (HPYs or HPRs) for an investment.
• How do you measure the mean annual return?
- Arithmetic Mean Return (AM)
- Geometric Mean Return (GM)
• Example 3
- Suppose you invested $100 three years ago and it is worth $110.40 today. The information
below shows the annual ending values and HPR and HPY. This example illustrates the
computation of the AM and the GM over a three-year period for an investment.
,AM = [(0.15) + (0.20) + (-0.20)]/3
= 0.15/3
= 5%
GM = [(1.15) + (0.20) + (-0.20)]1/3 – 1
= (1.104)1/3 – 1
= 1.03333 – 1
= 3.35%
Comparison of AM and GM
• When rates of return of the same for all years, the AM and the GM will be equal.
• When rates of return are not the same for all years, the AM will always be higher than the GM
• While the AM is best used as an “expected value” for an individual year, while the GM is the best
measure of an assets long-term performance.
A Portfolio of investments
• The mean historical rate of return (HPY) for a portfolio of investments is measured as the weighted
average of the HPYs for the individual investments in the portfolio, or the overall percentage
change in value of the original portfolio
• The weights used in computing the averages are the relative beginning market values for each
investment
• This is referred to as dollar-weighted or value-weighted mean rate of return
Exhibit 1.1
• Market weight are based on beginning vales → Beginning market value/total beginning market
value = market weight
Calculating Expected Rates of Return
• Risk is the uncertainty of the future outcomes of an investment
, - There are many possible returns or outcomes from an investment due to the uncertainty
- Probability is the likelihood of an outcome
- The sum of the probabilities of all the possible outcomes is equal to 1.0
• The expected return from an investment is defined as:
Measuring risk
• Statistical measures allow comparison of the return and risk measures for alternative investments
directly
• Two possible measures of risk (uncertainty) have received support in theoretical work on portfolio
theory:
- Variance
- Standard deviation of the estimated distribution of expected returns
