MODULE 5: RISK, RETURN & PORTFOLIO MANAGEMENT
Risk and return
The greater the risk, the larger return required by investors for compensation for
bearing that risk. Higher risk also means less certainty or greater volatility
Return is the benefit an investor receives/earns from an investment
Total Holding Period Return
Return on shareholder investment, is made up of two components
1. Capital gains/losses – arising from price changes
2. Investment income/dividend yield – dividend or interest received
[ ( 𝑃1 − 𝑃0 ) + 𝐷 ] × 100
=
𝑃0
Risk and return measures, using historical data
Year Actual Returns Average return Deviations from mean Deviation squared
𝑅 𝑅̅ 𝑅 − 𝑅̅ (𝑅 − 𝑅̅)2
Mean = Total Annual Returns ÷ no. of years
Variance = Total Deviations Squared ÷ (no. of years -1)
Standard deviation = [Variance]0.5
Risk and return measures, using forecast data
Economic Probability Actual Expected Deviation Deviation
state return return squared
𝑝 𝑅 𝑝 × 𝑅 𝑅 − 𝐸[𝑅] 𝐷𝐸𝑉 2 𝑝 × 𝐷𝐸𝑉 2
Expected Return = Sum of p x R
Variance = Sum of p x DEV2
Standard deviation = [p x DEV2]0.5
Interpretation
Normal distribution
symmetric frequency distribution that is completely described by its mean or
expected return and standard deviation
its left and right sides are mirror images of each other and:
the mean falls directly at the centre of the distribution
the probability that an outcome is a particular distance from the mean is the
same whether the outcome is on the left or right side of the distribution
the standard deviation tells us the probability that an outcome will fall within a
particular range or a particular distance from the mean
No. of standard Confidence level Formula for calculating the interval
deviations from mean (min & max)
1.000 68.26% E[RA] +/- (𝜎 × 1.000)
1.645 90% E[RA] +/- (𝜎 × 1.645)
1.960 95% E[RA] +/- (𝜎 × 1.960)
2.575 99% E[RA] +/- (𝜎 × 2.575)
Risk and return
The greater the risk, the larger return required by investors for compensation for
bearing that risk. Higher risk also means less certainty or greater volatility
Return is the benefit an investor receives/earns from an investment
Total Holding Period Return
Return on shareholder investment, is made up of two components
1. Capital gains/losses – arising from price changes
2. Investment income/dividend yield – dividend or interest received
[ ( 𝑃1 − 𝑃0 ) + 𝐷 ] × 100
=
𝑃0
Risk and return measures, using historical data
Year Actual Returns Average return Deviations from mean Deviation squared
𝑅 𝑅̅ 𝑅 − 𝑅̅ (𝑅 − 𝑅̅)2
Mean = Total Annual Returns ÷ no. of years
Variance = Total Deviations Squared ÷ (no. of years -1)
Standard deviation = [Variance]0.5
Risk and return measures, using forecast data
Economic Probability Actual Expected Deviation Deviation
state return return squared
𝑝 𝑅 𝑝 × 𝑅 𝑅 − 𝐸[𝑅] 𝐷𝐸𝑉 2 𝑝 × 𝐷𝐸𝑉 2
Expected Return = Sum of p x R
Variance = Sum of p x DEV2
Standard deviation = [p x DEV2]0.5
Interpretation
Normal distribution
symmetric frequency distribution that is completely described by its mean or
expected return and standard deviation
its left and right sides are mirror images of each other and:
the mean falls directly at the centre of the distribution
the probability that an outcome is a particular distance from the mean is the
same whether the outcome is on the left or right side of the distribution
the standard deviation tells us the probability that an outcome will fall within a
particular range or a particular distance from the mean
No. of standard Confidence level Formula for calculating the interval
deviations from mean (min & max)
1.000 68.26% E[RA] +/- (𝜎 × 1.000)
1.645 90% E[RA] +/- (𝜎 × 1.645)
1.960 95% E[RA] +/- (𝜎 × 1.960)
2.575 99% E[RA] +/- (𝜎 × 2.575)
