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?

M.Mukwena

Why Do Individuals Invest ?

2 choices with your earnings:  Save and tradeoff present consumption for a larger future consumption  Riskier option of investments M.Mukwena

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 M.Mukwena

Pure Rate of Interest Consumption Today Versus Tomorrow Trade-Off

ZMK 5 ZMK 5 ZMK 4 ZMK 4 ZMK 3 ZMK 3 ZMK 2 ZMK 2 ZMK 1 ZMK 1 ZMK 0 ZMK 0 ZMK 10 ZMK 20 ZMK 30 ZMK 40 ZMK 50 Consumption M.Mukwena

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 M.Mukwena

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% M.Mukwena

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 M.Mukwena

Measures of Historical Rates of Return

Holding Period Return HPR  Ending Value of Investment Beginning Value of Investment  K220 K200  1 .

10 K220 after 1 holding period.

beginning worth K200 M.Mukwena

Measures of Historical Rates of Return

Holding Period Yield HPY = HPR - 1 1.10 - 1 = 0.10 = 10% M.Mukwena

Measures of Historical Rates of Return

Investment cost K250 and is worth K350 after 2 years holding period.  HPR= 350 250 years = 1.40 Note this is for 2   Annual HPR= 𝐻𝑃𝑅 1/𝑛 1.1832

1.40

1/2 Annual HPY = Annual HPR-1= 1.1832-1=0.1832

= M.Mukwena

Measures of Historical Rates of Return

Arithmetic Mean AM where :   HPY/

n

 HPY  the sum holding of annual period yields M.Mukwena

Measures of Historical Rates of Return

Geometric Mean GM    HPR  1

n

 1   the product of annual HPR M.Mukwena

Measures of Historical Rates of Return Year 1 2 3 Beginning Value of Investment

100 115 138

End Value of Investment

115.0

138.0

110.4

HPR

1.15

1.20

0.8

HPY

0.15

0.2

-0.2

   From given table AM= 0.15+0.2−0.2

3 =0.05

GM= [ 1.15 1.20 0.8 ] 1/3 = 0.03353 M.Mukwena

B

Inv

A

Arithmetic Mean versus Geometric Mean beg Y1 Y2 HPR

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

HPY

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

AM GM

1+(−0.5) 2 =0.25 [ (2 0.5 ] 1/2 =0 -1 10 8 12 Yr1: 8/10=0.8

Yr2: 12/8=1.5

Yr1: 0.8-1=-0.2

Yr2:1.5-1=0.5

−0.2 +0.5

0.15

2 [0.8 1.5 ] 1/2 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 M.Mukwena

Portfolio of Investments

The mean historical rate of return for a portfolio portfolio. Example to follow of investments is measured as the weighted average of the HPYs for the individual investments in the M.Mukwena

Computation of Holding Period Yield for a Portfolio

Stock A B C Total Shares 100,000 200,000 500,000 Begin Price K10 K20 K30 Beginning Ending Mkt. Value Price 1 000 000 4 000 000 15 000 000 K20 000 000 K12 K21 K33 Ending Mkt. Value 1 200 000 4 200 000 16 500 000 K21 900 000 HPR HPY 1.20 20% 1.05 5% 1.10 10% HPR = K21 900 000 K20 000 000 = 1.095

HPY = 1.095- 1 = = 0.095

9.5% *Market Wtd.

Weight HPY 0.05 0.010 0.20 0.010 0.75 0.075 0.095 *Market Weights based on Beginning Mkt Value M.Mukwena

Expected Rates of Return

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

i n

  1 ( Probabilit y of Return)  (Possible Return) M.Mukwena

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 M.Mukwena

Probability Distributions

Risk-free Investment

1,00 0,80 0,60 0,40 0,20 0,00 -5% 0% 5% 10%15%

Return M.Mukwena

Probability Distributions

Risky Investment with 3 Possible Returns

1.00

0.80

0.60

0.40

0.20

0.00

-30% -10% 10% 30%

Return M.Mukwena

Probability Distributions

Risky investment with ten possible rates of return 1.00

0.80

0.60

0.40

0.20

0.00

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

M.Mukwena

Measuring the Risk of Expected Rates of Return

Variance (  )  i n   1 ( Probabilit y)  (Possible Return Expected Return) 2

i n

  1 ( P i )[R i  E(R i )] 2 M.Mukwena

Measuring the Risk of Expected Rates of Return

Standard Deviation is the square root of the variance M.Mukwena

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

  i E(R) M.Mukwena

Measuring the Risk of Expected Rates of Return

Expected Return Standard Deviation

Investment A

0.07

0.05

Coefficient of Variation 0.05/0.07 = 0.714

Investment B

0.12

0.07

0.07/0.12 = 0.583

B has less risk per unit and is therefore better investment M.Mukwena

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 M.Mukwena

Nominal Risk-Free Rate

 Rate of interest stated in money terms  Dependent upon ◦ Conditions in the Capital Markets ◦ Expected Rate of Inflation M.Mukwena

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

M.Mukwena

Systematic Risk

 Business risk  Financial risk  Liquidity risk  Exchange rate risk  Country risk M.Mukwena

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?

M.Mukwena

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.

M.Mukwena

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) M.Mukwena

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 M.Mukwena

Security Market Lines

Rateof Return (Expected) Low Risk Average Risk High Risk Security Market Line RFR The slope indicates the required return per unit of risk Risk (business risk, etc., or systematic risk-beta) M.Mukwena

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

Expected Rate Security Market Line RFR Movements along the curve that reflect changes in the risk of the asset Risk (business risk, etc., or systematic risk-beta) M.Mukwena

Change in Market Risk Premium

Rm'

´

New SML Original SML M.Mukwena

Risk

Capital Market Conditions, Expected Inflation, and the SML

New SML Original SML M.Mukwena

Risk