BF 320: Investment

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BF 320 Investment Portfolio Management
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Investment Setting

• Objectives
• Why do individuals invest? What is an investment?
• How do we measure the rate of return on an
  investment?
• How do investors measure risk related to
  alternative investments?
• What macroeconomic and microeconomic factors
  contribute to changes in the required rate of
  return for investments?

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Why Do Individuals Invest ?

• 2 choices with your earnings
• Save and tradeoff present consumption for a
  larger future consumption
• Riskier option of investments

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Required Rate Of Return

• The pure rate of interest is the exchange rate
  between future consumption and present
  consumption. Market forces determine this rate.
• Ex if you can exchange K5 of certain income
  today for K50 tomorrow this rate is 5/5010.
  AKA pure time value of money

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Pure Rate of Interest
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Required Rate Of Return

• 2. 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.
• Ex Investor in Zambia would expect 7
  compensation for inflation

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Required Rate Of Return

• 3. 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.
• Ex A return of 2
• Therefore from above examples an investor would
  need compensation of 1072 19

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Defining an Investment

• A current commitment of money (K) 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.
• These three make up required rate of return

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Measures of Historical Rates of Return

• Holding Period Return

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Measures of Historical Rates of Return
Holding Period Yield HPY HPR - 1 1.10 - 1
0.10 10
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Measures of Historical Rates of Return

•  

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Measures of Historical Rates of Return

• Arithmetic Mean

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Measures of Historical Rates of Return

• Geometric Mean

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Measures of Historical Rates of Return

•  

Year Beginning Value of Investment End Value of Investment HPR HPY
1 100 115.0 1.15 0.15
2 115 138.0 1.20 0.2
3 138 110.4 0.8 -0.2
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Arithmetic Mean versus Geometric Mean
For A the AM is not true (25) since
investment went from 10 to 20 to 10. Therefore GM
is better measure. For B 10(1.15)(1.15)13.23
which should be 12. However 10(1.0954)(1.0954)12.
Therefore GM is better measure
Inv beg Y1 Y2 HPR HPY AM GM
A 10 20 10 Yr120/102 Yr210/200.5 Yr1 2-11 Yr2 0.5-1-0.5
B 10 8 12 Yr1 8/100.8 Yr2 12/81.5 Yr1 0.8-1-0.2 Yr21.5-10.5
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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. Example to follow

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Computation of HoldingPeriod Yield for a
Portfolio
Begin Beginning Ending Ending Market Wtd.
Stock Shares   Price   Mkt. Value   Price   Mkt. Value HPR HPY Weight HPY
A 100,000 K10 1 000 000 K12 1 200 000 1.20 20 0.05 0.010
B 200,000 K20 4 000 000 K21 4 200 000 1.05 5 0.20 0.010
C 500,000 K30 15 000 000 K33 16 500 000 1.10 10 0.75 0.075
Total K20 000 000 K21 900 000 0.095

HPR K21 900 000 1.095
HPR K20 000 000 1.095

HPY 1.095- 1 0.095

9.5
Market Weights based on Beginning Mkt Value
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Expected Rates of Return

• Risk is uncertainty that an investment will earn
  its expected rate of return
• Probability is the likelihood of an outcome

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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

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Probability Distributions

• Risk-free Investment

Probability
Return
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Probability Distributions

• Risky Investment with 3 Possible Returns

Probability
Return
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Probability Distributions

• Risky investment with ten possible rates of return

Probability
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Measuring the Risk of Expected Rates of Return
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Measuring the Risk of Expected Rates of Return

• Standard Deviation is the square root of the
  variance

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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

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Measuring the Risk of Expected Rates of Return
Investment A Investment B
Expected Return 0.07 0.12
Standard Deviation 0.05 0.07

Coefficient of Variation 0.05/0.07 0.714 0.07/0.12 0.583
B has less risk per unit and is therefore better investment
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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
• Take note RRFR was earlier called pure time
  value of money as only sacrifice investor made
  was deferring use of money

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Nominal Risk-Free Rate

• Rate of interest stated in money terms
• Dependent upon
• Conditions in the Capital Markets
• Expected Rate of Inflation

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Adjusting For Inflation

• Nominal RFR
• (1Real RFR) x (1Expected Rate of Inflation)
  1
• Ex If you require a real growth in the
  purchasing power of your investment of 8, and
  you expect the rate of inflation over the next
  year to be 3, what is the lowest nominal return
  that you would be satisfied with? (10.08) x
  (10.03) - 1 0.1124

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Systematic Risk

• Business risk
• Financial risk
• Liquidity risk
• Exchange rate risk
• Country risk

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Systematic Risk

• Business Risk
• Uncertainty of income flows caused by the nature
  of a firms business
• Sales volatility and operating leverage determine
  the level of business risk.
• Financial Risk
• Uncertainty caused by the use of debt financing.
• AKA leveraging risk
• 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
  stocks risk premium.
• Q Does a company utilizing only common stock to
  finance their investments suffer financial risk?

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Systematic Risk

• 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.

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Systematic Risk

• 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
• f (Business Risk, Financial Risk, Liquidity Risk,
  Exchange Rate Risk, Country Risk)

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Systematic Risk

• 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

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Security Market Lines
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Changes in the Required Rate of Return Due to
Movements Along the SML
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Change in Market Risk Premium
Expected Return
Rm
Rm
NRFR
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Capital Market Conditions, Expected Inflation,
and the SML