Portfolio Inv

7/28/2019 Portfolio Inv

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PORTFOLIO INVESTMENT.

Uncertainty vs Risk - a distinction is usually made between the two

terms;-

Uncertainty is defined as the situation where various cash flow patterns

are possible but probabilistic information is absent or at least incomplete.

Risk, however is defined as a situation where the parameters of the

probability distribution of outcomes are known, ie normally distributed

about a mean average return.

RETURN - The return from holding an investment (share) over someperiod of time (more than a year), is simply any cash payments received

due to ownership (dividends), plus the change in the market price (capital

gains), divided by the original purchase price (to give a %);-

Return =pricebegining

price)begining-price(endingpaid)(dividends +

1

100

ie;- R = Dt + ( Pt - Pt-1 ) 100

Pt-1 1

Research shows that investors in financial securities demand higher

returns from risky investments in equities than from comparatively risk-

free government securities.

Investors rarely place their entire wealth into a single asset or investment.

Rather, they construct a portfolio, (a combination of two or more

securities or assets), of investments.

When we begin with a single stock, the risk of the portfolio is thestandard deviation of that one investment. As the number of randomly

selected stocks held in the portfolio is increased, the total risk of the

portfolio is reduced. Such a reduction is at a decreasing rate however.

Thus, a substantial proportion of the portfolio risk can be eliminated with

a relatively moderate amount of diversification, usually with 15 to 20

randomly selected stocks.


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standard

deviation

of

portfolio

return

Unsystematic

risk

Total Systematic

risk risk

15/20

Number of Securities in Portfolio.

Systematic (Market) Risk- Risk due to factors that affect the overall

market, such as changes in the nations economy, tax changes by the

government, changes in the worlds energy situation, etc. These are risks

that affect securities overall, consequently, they cannot be diversified

away.

Unsystematic (Unique) Risk- Risk unique to a particular company or

industry, (ie. it is independent of economic, political, etc. factors which

affect all securities in a systematic manner), typically involving - strikes

at one company, increased competition in the market, etc. This type of

risk can be reduced and even eliminated if diversification is efficient.

TOTAL RISK = SYSTEMATIC RISK + UNSYSTEMATIC RISK

(non-diversifiable) (diversifiable)

If the unsystematic (unique) risk can be diversified away through

increasing the portfolio assets, then the only risk left is the systematic

(market) risk. In this situation, individual risky assets will be priced by

reference to their relationship to the market generally, ie. on the basis of

their market risk alone. Therefore, it is the covariance of the individual

securities with the market which is now the appropriate measure of risk.

This measure of risk is called BETA and is represented by the Greeksymbol .


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BETA ( ) - An index of systematic risk. It measures the sensitivity of a

stocks returns to changes in the returns on the market portfolio. The beta

of a portfolio is simply a weighted average of the individual stock betas

in the portfolio.

Excess return

On stock +ve >1 (aggressive)

=1


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The Security Market Line - Describes the relationship between an

individual securitys required return and its systematic risk, as measured

by beta;-

Security market line

Expected

Return

Risk premium

Rm

Rf

Risk-free return

0

1.0

Systematic Risk (BETA)

Returns and Stock Prices - The Capital Asset Pricing Model provides a

means by which to estimate the expected rate of return on a security. This

return can then be used as the discount rate in a dividend-valuation

model. The intrinsic value of a stock can be expressed as the present

value of the stream of expected future dividends;-

V = =

= +

t

1t e

t

t

)K(1

D

Where;- tD = the expected dividend in period t.

eK = the expected rate of return for the stock.


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If however, it is believed that there will be a perpetual increase (growth)

in the future dividends, the above model can be modified to a more

common (and simpler) form;-

V =g-K

D

e

1

Where;- V = value of the stock.

D1 = the expected rate of return in period 1.

Ke = the expected rate of return for the stock.

g = the expected future growth in dividends per share.

SUMMARY;-

1) Rj = Rf + j (Rm Rf).

2) V =g-K

D

e

1

(NOTE:- For all practical purposes the Required Rate of Return is the

same as the Expected Rate of Return, ie.- Rj = Ke.)

Portfolio Inv

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