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### Ch: 11- Return and Risk: CAPM

Realized return

Expected Return

Individual Security Risk

Covariance and Correlation

Portfolio Expected Returns

Diversification Effect

Portfolio Risk and CAPM

Realized Return

- Investors earn returns from stocks in two forms: Dividends, Capital gains
- Realized Return in dollars = Dividend + (Price1 – Price0)
- Rate of Realized Return = Dividend yield + Capital yield
- R = (D/P0) + (P1-P0)/P0 = (D + P1 – P0)/P0
- Another name for realized return is “Holding period return”

Expected Return

- Expected return is the average return an investor can expect from a stock in the future
- List all the possible returns and find their average to calculate expected return
- This example suggests that all the possible outcomes have equal chance of happening
- If not then probability of each occurrences have to be found and assigned as weights.
- Weighted average of the individual returns would give the expected return

Individual Security Risk

- There is uncertainty over expected rate
- This uncertainty is the risk of the stock
- Risk is measured by variance and standard deviation.
- Measure of how much the return will change or deviate from the expected
- Variance = Standard Deviation squared

Covariance and Correlation

- The relationship between return of one stock with the other can be measured with: Covariance and correlation
- Negative values for both measures means the returns are opposite to each other
- Positive values for both measures mean the returns are similar or close to each other.
- Correlation ranges in between -1 & 1, whereas covariance can be of any value

Portfolio Expected Return

- In Summary:
- What happens if an investor invests in both these companies and create a portfolio of investment?

Portfolio Expected Return

- If an investor who has $100 invests $60 in supertech and the rest in slowpoke then what is the portfolio expected return he will earn?
- R = [(60/100) X 17.5] + [(40/100) X 5.5]

= 12.7%

- Expected portfolio return is the weighted average of the individual stocks’ returns. The weights are based on the portion of total investment in each stock

Diversification Effect

- Weighted Average Standard Deviation =

(0.6 X 0.2586) + (0.4 X 0.115) = 20.12%

- Unlike expected return, the risk of a portfolio is not the weighted average of the individual stocks’ risks.
- The weighted average calculation does not take into account the covariance and correlation in between the stocks.
- Whenever a portfolio is created there is a diversification effect due to the correlation.

Diversification Effect

- Negative correlation of two stocks mean when one is giving negative return the other is giving positive return and vice versa.
- Thus a portfolio of the two stocks will minimize the risk of loss as the positive stock will cover the losses of the negative stock
- This is the diversification effect of a portfolio

Diversification Effect

- Systematic and Unsystematic Risk:
- Systematic Risk is any risk that affects a large number of assets, each to a greater or lesser degree.
- Macroeconomic risks associated with the entire market
- Cannot be minimized through diversification
- Unsystematic Risk is a risk that specifically affects a single asset or a small group of assets
- Stand-alone risk due to the specific news and information available about an asset.
- Measured with Variance and Standard Deviation
- Can be completely removed through diversification

Portfolio Risk and CAPM

- Unsystematic risk can be removed through addition of more stocks
- So, Standard Deviation of portfolio is unimportant since it can be zero with enough number of shares
- Systematic Risk is the only risk associated with a portfolio and it is the only one an investor should be worried about
- Can be measured with Beta.

Portfolio Risk and CAPM

- Beta is a ratio of change in market return with changes in stock’s return

Portfolio Risk and CAPM

Slope of a graph with Return on Stock at X-axis and Return on Market in Y-axis is the Beta for the stock.

OR

The following formula can also be used to find Beta:

Portfolio Risk and CAPM

- Return from any asset should be able to compensate for all risks, through risk premiums, and still make profit.
- Thus R = Profit + Risk Premium
- Profit is the return at risk-free rate that can be achieved from a security without any risk
- For bond returns Rb = Rf + RPb
- For stock market return Rm = Rf + RPm
- For an individual stock return Rs = Rf + RPs

Portfolio Risk and CAPM

- Since systematic risk is the only risk associated with a stock that needs compensation, and that risk depends on the market’s risk
- Thus RPs = β X RPm
- OR RPs = β X (Rm – Rf)
- Therefore, Rs = Rf + β(Rm – Rf)
- This is the Capital Asset Pricing Model (CAPM) used to find the required return of a stock.
- When required return equals expected return market is said to be at equilibrium

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