©2015, College for Financial Planning, all rights reserved.

Session 3Types & Measurements of Risk, Standard Deviation, Beta, CAPM

CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAMInvestment Planning

Session Details

Module 2

Chapter(s)

1, 2, 3

LOs 2-3 Calculate a weighted average return. Also calculate the standard deviation and mean return of a single asset, and understand how the range of returns is calculated within one, two, and three standard deviations.

2-4 Calculate coefficient of variation, and understand its application.

2-8 Calculate required return using the capital asset pricing model (CAPM), and understand its application.

3-2

Risk

• Standard deviation: variability• Beta: volatility

3-3

Standard Deviation

Mean Return10%

+2 σ+1 σ-1 σ +3 σ-2 σ-3 σ

M (mean/average return) = 10%σ (standard deviation) = 15%

(Normal Distribution)

25% 40% 55%- 5%- 20%- 35%

68% of returns

95% of returns

99% of returns

2-4

Standard Deviation• For normally distributed returns, calculate the

standard deviation range, add and subtract the standard deviation amount from the mean return.Example: Mean return of 10%, Std deviation of 15%

• One standard deviation: 10 + 15 = +25, and 10 – 15 = – 5

• Two standard deviations: 25 + 15 = +40, and – 5 – 15 = – 20

• Three standard deviations: +55 to -353-5

Standard Deviation Concepts

• Normal distribution • Skewness (security

returns are positively skewed)

• Kurtosis• Leptokurtic• Platykurtic

3-6

Standard Deviation Question

Scorpio Inc. has a mean return of 19%, and a standard deviation of 25.

What is the probability that the stock will have a return greater than 19% if the returns are normally distributed?

3-7

Standard Deviation Question

Libra Inc. has a mean return of 11%, and a standard deviation of 9.

Assuming the returns are normally distributed, what is the probability that the stock will have a return greater than 20%?

3-8

Standard Deviation of a Single Asset

Use the calculator!

1 n

)r (r

2n

3-9

Calculating Standard Deviation

Single Asset (2)

• Formula #4 on diagram • Calculation is simple on

the 10BII+ or 12C

Assume Acme Industries has the following annual returns:• + 15%• + 22%• - 7%• + 10%What is the standard deviation and mean return?

3-10

Calculating Standard Deviation

Single Asset (2)

Keystrokes are: 1, SHIFT, P/YR 15, ∑+ 22, ∑+ 7, +/-, ∑+ 10, ∑+ SHIFT, 8 (g, “.” on 12C) Answer = 12.36

For the mean return the keystrokes would be: SHIFT, 7 (g, “0” on 12C) Answer = 10%

3-11

Coefficient of Variation

Risk per unit of return

x

σCV

3-12

Coefficient of Variation Example

CV(A) = 6%/10% = 0.60CV(B) = 9%/12% = 0.75B has a higher mean, but also has a higher CV, which means you take higher risk per unit of return.

Remember that you can easily calculate both standard deviation and mean return for a single asset with your financial calculator, as we did previously.

Asset A Asset B

Std Dev. 6% 9%

Mean. 10% 12%

3-13

Beta Coefficients

• Measures the volatility of a stock (or portfolio) relative to the market (a benchmark); so, the greater the correlation, the more accurate beta becomes.

• Since R-squared measures systematic risk, it can be used to determine beta reliability; generally you are looking for an R-squared of 70 or higher in order for beta to be considered reliable. ββ

3-14

Beta

Beta of 1 means the asset has the same volatility as the benchmark.What would be the approximate price movement of the Acme Fund if it has a beta of .85, and the benchmark it is being compared to has a return of 15%?Answer: 15% x .85 = 12.75%

What if Acme’s beta were 1.25?Answer: 15% x 1.25 = 18.75%

3-15

Weighted Average Using Beta

What is the weighted beta of the following portfolio?

• $40,000 in AAA, beta of 1.2

• $20,000 in TTT, beta of 0.9

• $15,000 in ZZZ, beta of 0.8

Shortcut on 10BII+ calculator:

1.2, INPUT (ENTER on 12C)

40,000, ∑+

.9, INPUT

20,000, ∑+

.8, INPUT

15,000, ∑+

SHIFT, 6 (g, 6 on 12C) Answer = 1.043-16

The Capital Asset Pricing Model

• CAPM also has a micro component that looks at individual stock returns – the Security Market Line – SML

• This micro component is also used to help value stocks

)βr(rrr fmf

3-17

The Capital Asset Pricing Model

The risk-free rate is 3.5%, and the market’s expected return is 8%. Your stock has a beta of 1.1.

What is the required return?• r = 3.5 + (8.0 – 3.5)1.1• r = 3.5 + 4.95• r = 8.45

What is the market risk premium?• 4.5% (8.0 – 3.5)

3-18

Required Return Calculations

What is the required return for the following securities? The risk-free rate is 4%, and the market return is 8%.

Fund BetaRequired Return

Triad 0.9

Triangle 1.1

Trapeze 2.0

Tango 1.4

Tangent 1.0

3-19

Question 1

Jake wants to know the beta coefficient for his portfolio of stocks, shown below:

What is the beta coefficient for Jake’s portfolio?

a. 1.14b. 1.19c. 1.23d. 1.28

StockCurrent Market

Value Beta

Alto Associates $33,000 1.1

Bolero Enterprises $12,500 1.0

Cactus Co. $45,000 0.9

Dire Straights Int’l $29,000 1.6

3-20

Question 2

Triad Industries has a mean return for the past five years of 12%, with a standard deviation of 9%. Assuming the returns are evenly distributed, what is the probability that Triad will have a return greater than 21%?a. 3%b. 12%c. 16%d. 24%

3-21

Question 3

Your client has narrowed his choice down to the following three mutual funds, and wants your opinion concerning which one to choose based on the fund that will provide the lowest amount of risk per unit of return.

Which fund should your client choose?

a. Fund ABCb. Fund DDDc. Fund EFG

FundMean Return

Standard Deviation

ABC 8% 12

DDD 10% 14

EFG 7% 10

3-22

Question 4

A mutual fund you are considering has a beta of 0.75, a standard deviation of 11, a correlation coefficient of .90 with the Russell 2000, an R-squared of .65 with the S&P 500, and an expected return of 12%. Which one of the following is the fund’s coefficient of variation?a. .92b. 1.09c. 1.15d. 1.25

3-23

Question 5

The current return of the market is 11%. The current market risk premium is 7%, and the risk-free rate is 4%. If the beta of your stock is 1.1, what is your required return?a. 7.30b. 11.70c. 12.10d. 16.10

3-24

©2015, College for Financial Planning, all rights reserved.

Session 3End of Slides

CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAMInvestment Planning