10) Risk and Return

What is investment Risk

The change you may not make, or even lose, money on an investment

Investors must understand this to be able to make better comparative decisions

Risk - Return Relationships

Typically as risk is increased, return increases aswell

This is to incentivise investors to actually invest

Common Sense Rules

In the scenarios:

• Same Risk, Different Reward: Choose the higher reward

• Same Reward, Different Risk: Choose the lower risk

Risk Aversion and Tolerance

Risk Aversion:

• Risk aversion refers to the psychological tendancy to seek safer, guaranteed investments.

Risk Tolerance

• The level of risk an investor is willing to accept

• Can depend on factors such as financial circumstance, ability to handle loss, etc

Realised Return

The actual return earned over the period of an investment

Example:

• A shareholders realised return is the profit from dividends, and change in share price

Holding Period Return

The total rate of return from holding an investment over the given period

HPR = (P₁ - P₀ + D₁) / P₀ D = Total income from dividends over period

Difference when calculating expected returns

To calculate expected returns, use the expected P₁ and dividend values

Components of Total Return

TR = Capital Gains ( (P₁ - P₀) / P₀ ) + Dividend Yield ( (D₁) / P₀ )

Common Measures of Risk

Probability Distribution

Expected (Average) Return

Measures of Dispersion (Mean and Variance)

Probability Distribution

Risky investments often have several possible outcomes, with different chances for each

Probability distributions show these outcomes and their respective chances

Expected Return

Calculated as a weighted average of the possible returns

E(R) = (Return_A x Probabilitiy_A) + (R_B x P_B) + (R_C x P_C)

What are the 2 Measures of Dispersion

Variance

Standard Deviation

Variance (for distribution)

The standard deviation squared, showing the volitility of an investment

Calculating Variance with a Scenario

Found by the process:

• Subtract the average (Expected Return) from each possible return

• Square each difference

• Multiply each squared difference by respective probability

• dd the values together

Calculating Variance with Historical Data

Found by the process:

• Subtract the average (Expected Return) from each possible return

• Square each difference

• Add the squared deviations together

• Divide by N - 1

Standard Deviation

The square root of variance

Key measure for the total risk of a security

Measure the volitility of an investment (the higher, the more risky)

Using past data

The future probability distribution of an investment is often unkown

Hence we use past data to predict future performance

The two approaches of data analysis

Scenario Analysis

• Using given future predictions

Time-Series Analysus

• Using past data to predict future performance

The two types of sequences

Arithmetic (Annual Average Return)

Geometric (Realised Return)

Arithmetic Return

Sequence for the average return of a period

R = (R₁+R₂+R₃+R₄+R_N) / N

Geometric Return

Finds the real return of a period

G = ( (1+R₁)+(1+R₂)+(1+R₃)+(1+R_N) )^1/N - 1

Comparing Geometric vs Arthimetic Averages

Geometric returns are the real returns from a period

Arithmetic returns are the average of the returns of the period (often larger than geometiric)

Dividend Reinvestment

Holding a stock past its dividend reinvestment date, means you can reinvest it

We assume all dividends are reinvested

Hence, a stock paying quarterly dividends is calculated by:

• R_Annual = (1+R_q1)(1+R_q2)(1+R_q3)(1+R_q4) - 1

Interpreting Risk and Return

There are 3 types of investments (used by the lecture):

• Treasury Bills: Lowest Return, but Safest

• Small Stocks: Highest Return, but riskiest

• Large Stocks: Average in Both

Supports Risk vs Return theory

Key Restraints to note

Historical data doesn’t guarantee future results

The duration of an investment is also important, some may have short-term losses but long-run profit

Excess Returns and Risk Premiums

Excess return is the difference between an investment and it’s risk free alternative

• Excess Return = Investment Return - Risk Free Return

Risk premiums are additional expected returns required for accepting risk

• Relient on type of risk (Systematic vs Unsystematic)

• Only Systematic risk gives premium as it can’t be avoided

Divesification and Risk

Diversification refers to buying a range of unconnected stocks

This allows to mitigate most/all Unsystematic risk

This can be created through analysing correlation coefficients to find negatively correlated stocks

Types of Risk

UnSystematic (Risk associated with the company, can be diversified)

Systematic (Risk from the wider economic climate, cannot be diversified)

Total Risk = Systematic + UnSystematic

Systematic Risk and Beta

To measure systematic risk, we measure it’s affect on variability vs unsystematic risk

Beta measures how sensitive return is to change in the overall market

If a stocks return changes more than the market’s, it has a higher Beta

Interpreting Beta

If beta equals:

• 1: Moves With the Market

• >1: More sensitive than the market (beta acts as a multiplier)

• 0-1: Moves with the market, but not as sensitive

• 0: Uncorrelated to market change (cash doesnt change value)

• >0: Opposes the market (Gold)

Beta vs Std Deviation

Beta measures sensitivity, Std Deviation measures volatility

Beta focusses purely on systematic risk, StdD focusses on both

A firm can have a high Std Deviation, but a low Beta

Estimating Beta

By using the regression of a stock, and comparing aginst a market index (S&P 500)

Portfolio Beta

The weighted average of a portfolios betas

Weights are based on proportion of portfolio