# Unit 5 Notes: Risk and Return

Corporate Finance lecture notes for the EMBA at UNSW.

## Past returns

Investors achieve returns by 2 ways:

- Dividends received;
- Price gain/increase on shares;

Price gains linked to dividend growth

Price increase with expected future dividends;

Future profits and dividends increase because:

- Total economy is expanding (GDP);Prices are increasing (CPI);
- Industry’s profit share of economy is expanding;
- Firm’s profit share of industry is expanding;

**Dividend Yield**

Simple formula ignoring time value.

D = Total dividend in period P_{0}= Price at start

=

Which stock price to use?

Current yield = use current price; Period yield = use price at start of period

**Capital gains**

Percentage return from price increase

Holding period return rt or Past total returns on one share

=

= 0.104 = 10.4%

**Indices**

Index shows only the capital gains but not the dividend yield.

##### Future returns

How to account for uncertainty about the future

**Method 1: Use probability**

Define various scenarios or economic states and then subjective probability of each economic state of occurring.

Calculate expected value

Scenario 1: 25% probability of 30% return;

Scenario 2: 50% probability of 10% return;

Scenario 3: 25% probability of -10% return;

= 0.25 x 0.30 + 0.50 x .10 + 0.25 x – 0.10

= 0.10 or 10%

###### Method 2: Use CAPM

**Expected future returns of two assets**

E[r_{p}] = α_{1} x E[r_{1}] + α_{ 2 }x E[r_{2}]

E[r_{p}] = α_{ 1} x E[r_{1}] + (1- α_{ 1})x E[r_{2}]

**Expected future return of a portfolio**

Weighted average of expected stock returns:

E[r_{p}] = α_{ 1} x E[r_{1}] + α_{ 2 }x E[r_{2}] + α_{ 3} x E[r_{3}] + ..

α_{ 1} = % of stock 1 in portfolio based on $ value

α on all stocks must add to 100% or 1.00

If % weight of each stock is spread equal on a portfolio then α is dropped off and can use the average() expected returns of the portfolio

## Total Risk

3 types of risk

**1. ****Default risk**

Company goes bankrupt and shareholder get little. Shareholder returns ≈ -100%

**2. ****Total risk ****σ**

Standard deviation or average spread

Total Risk = Systematic risk + Unsystematic risk

**3. ****Systematic risk (****β)**

CAPM

**Measuring past total risk**

For an individual stock

- Calculate weekly returns based on prices;
- Calculate std dev of stock’s returns;

For portfolio of stocks (equal weights)

- Calculate weekly returns for each stock;
- Weekly portfolio returns = average of total stock;
- Calculate std dev of portfolio returns

Need to ‘annualise’ this standard deviation as it is based on weekly returns. Annualise by multiplying std dev of portfolio by √52.

## Portfolio Total Risk

Covariance = Measure of how two variables move together

Correlation coefficient = Measure the same thing as covariance but as a ratio

≈ 1 means strong relationship between the variables

The variance of 2-asset portfolio

- Must include relationship correlation coefficient

where

The definition of the correlation coefficient

The standard deviation

The weight * on the first asset in the **minimum variance portfolio**

where

## Diversification

Diversification allows portfolio to obtain:

The **return is equal** to weighted average of each component with **risk less than** the weighted average of each components

**Low covariance** is at the heart of diversification.

In 2 asset case, the degree of correlation (and hence covariance) was a key concept. The lower the correlation the greater the gains from diversification.

In N-asset case, the covariance is a key concept. The variance of a well diversified portfolio is the average covariance of the assets that make up the portfolio.

e.g. the correlation between assets is 0.5 and each asset has std deviation of 20% so the average covariance is (0.5)(0.2)(0.2) =0.02. The portfolio variance will decrease to 0.02 giving a standard deviation of 14.14%.

Disadvantage when the portfolio has very poor assets.

Correlation and covariance may be very high – sub prime mortgages. Individual component are high risk but in a portfolio the risk is reduced.