BF 320: Investment & Portfolio Management M.Mukwena.

M.Mukwena

BF 320: Investment & Portfolio Management

M.Mukwena

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

1. 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 5/50=10%. AKA pure time value of money

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Pure Rate of Interest

0 10 20 30 40 50ZMK 0

ZMK 1

ZMK 2

ZMK 3

ZMK 4

ZMK 5

Consumption Today Versus Tomorrow Trade-Off

Consumption

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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 10%+7%+2% =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

K200 worth beginning

period. holding 1after K220

10.1 K200

K220

Investment of Value Beginning

Investment of Value EndingHPR

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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

Investment cost K250 and is worth K350 after 2 years holding period. HPR= = 1.40 Note this is for 2 years

Annual HPR= = 1.1832Annual HPY = Annual HPR-1= 1.1832-1=0.1832

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Measures of Historical Rates of Return

Arithmetic Mean

yields period holding annual of sum the HPY

:whereHPY/AM

n

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Measures of Historical Rates of Return

Geometric Mean

HPR annual

ofproduct the

1 HPR GM 1

n

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Measures of Historical Rates of Return

From given tableAM= =0.05GM= = 0.03353

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

Inv beg

Y1

Y2

HPR HPY AM GM

A 10 20 10 Yr1:20/10=2Yr2:10/20=0.5

Yr1: 2-1=1Yr2: 0.5-1=-0.5

=0.25 [ -1 =0

B 10 8 12 Yr1: 8/10=0.8Yr2: 12/8=1.5

Yr1: 0.8-1=-0.2Yr2:1.5-1=0.5

0.15 -1=0.0954

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

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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

*Market Weights based on Beginning Mkt Value

Begin BeginningEndin

g 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 1.2020% 0.05

0.01

0

B

200,000 K20 4 000 000 K21 4 200 000 1.05 5% 0.20

0.01

0

C

500,000 K30 15 000

000 K33 16 500

000 1.1010% 0.75

0.07

5

Total K20 000

000 K21 900

000

0.09

5

HPR =

K21 900 000

= 1.095 K20 000

000

HPY = 1.095- 1 = 0.095

= 9.5%

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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

n

i 1

Return) (Possible Return) ofy Probabilit(

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Risk AversionThe 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

-0.05 0 0.05 0.1 0.150.000.200.400.600.801.00

Pro

bability

Return

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Probability Distributions

Risky Investment with 3 Possible Returns

0.00

0.20

0.40

0.60

0.80

1.00

-30% -10% 10% 30%Return

Pro

bability

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Probability Distributions

Risky investment with ten possible rates of return

0.00

0.20

0.40

0.60

0.80

1.00

-40% -20% 0% 20% 40%

Pro

bability

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Measuring the Risk of Expected Rates of Return

2n

1i

Return) Expected-Return (Possibley)Probabilit(

)( Variance

2iii

1

)]E(R)[RP(

n

i

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Measuring the Risk of Expected Rates of Return

Standard Deviation is the square root of the variance

n

i 1

2iii )]E(R-[RP

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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

E(R)i

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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 = (1+Real RFR) x (1+Expected 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? (1+0.08) x (1+0.03) - 1 = 0.1124

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Systematic RiskBusiness riskFinancial riskLiquidity riskExchange rate riskCountry risk

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Systematic 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.• 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 stock’s 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

Rateof Return

Risk(business risk, etc., or systematic risk-beta)

RFR

SecurityMarket LineLow

RiskAverageRisk

HighRisk

The slope indicates therequired return per unit of risk

(Expected)

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Changes in the Required Rate of Return Due to Movements Along the SML

Rate

Risk(business risk, etc., or systematic risk-beta)

RFR

SecurityMarket Line

Expected

Movements along the curvethat reflect changes in therisk of the asset

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Change in Market Risk Premium

Risk

RFR

Original SML

New SML

Rm

Rm'

E(R)

NRFR

Expected Return

Rm´

Rm

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Capital Market Conditions, Expected Inflation, and the SML

Risk

RFR

Original SML

New SMLRate of Return

RFR'

NRFR

NRFR´

Expected Return