Investment Returns and Risk: Means, Weighted Returns, IRR, Scenario Analysis - Prof. Eric , Study notes of Investment Theory

Download Investment Returns and Risk: Means, Weighted Returns, IRR, Scenario Analysis - Prof. Eric and more Study notes Investment Theory in PDF only on Docsity!

Investments

Risk and Returns: Part I

Chapter 5

Outline

 (^) Measuring returns

 (^) Historical returns

 (^) Measuring risk

 (^) Portfolio returns and risk

 (^) Modern portfolio theory

Arithmetic Mean Return

 (^) Simple average over multiple periods

 (^) Gives you expected return for a period

where rt = holding period return in period t

n = number of periods

n

r r r r r

n

r

r

t (^) n

 1 2 3 4 ...

Geometric Mean Return

 (^) Compound average return assuming one initial

investment and reinvestment of dividends

 (^) Calculates investment growth over time

1

n

PV

FV

r

  1  1  1  (^) ... 1  (^1)

1

1 2 3

n n r   1 r  1 r  1 r  ... 1 r  1

1

1 2 3      n  n r r r r r

Beardstown Ladies

Link to story.

Multi-Period Returns Example

 (^) You invest $1.0 in a fund which returns 10%,

25%, -20% and 25% over the next three years.

 (^) At the end of the first year you plan on investing

an extra $0.1, at the end of the second year you

invest an extra $0.5, at the end of the third year

you withdrawal $0.8, and at the end of the fourth

year you withdrawal the entire account balance.

 (^) Calculate arithmetic, geometric and dollar

weighted returns.

Expected Returns

 (^) To make estimates of future or expected

returns [ E(r) ], two common methods are …

 (^) Arithmetic mean return

• E(r) = (r 1 + r 2 + … + rn) / n

 (^) Scenario returns

• E(r) = p 1 r 1 + p 2 r 2 + p 3 r 3 + …
• Where^ pt = probability of scenario “t” occurring

r 1 = returns in scenario “t”

• all p’s must add up to 1

Scenario Returns Example

 (^) Develop a forecast of future stock returns,

assuming a 10% chance the economy goes

into recession where returns will be -25%, a

70% chance the economy will remain steady

where returns will be 5%, and a 20% chance

the economy goes into a boom where returns

will be 30%.

Measuring Risk

 (^) Risk measured as sample variance (σ (^2) ) or

sample standard deviation (σ) of returns.

r r ... r 2

2

T

2

2

2

1

T

r r r

σ

r r ... r

2

T

2

2

2

1

T

r r r σ

Historical Returns

Geom. Arith. Stan.

Series Mean% Mean% Dev.%

World Stk 9.41 11.17 18.

US Lg Stk 10.23 12.25 20.

US Sm Stk 11.80 18.43 38.

Wor Bonds 5.34 6.13 9.

LT Treas 5.10 5.64 8.

T-Bills 3.71 3.79 3.

Inflation 2.98 3.12 4.

Distribution of Returns

Time Series of Returns

Portfolio Variance (Two Assets)

19

 p

2 = w 1

2  1

**2

• w 2**

2  2

**2

• 2w 1 w 2 Cov(r 1, r 2 )**

where  1 2 = Variance of Security 1

 2 2 = Variance of Security 2

Cov(r1,r 2 ) = Covariance of returns between

Securities 1 and 2

Investments (^) Measuring Returns and Risk

Covariance and the

Correlation Coefficient

20

where 1,2 = Correlation coefficient between 1 and 2

Cov(r 1, r 2 ) =  1,  1  2

Investments (^) Measuring Returns and Risk

• (^) -1.0 ≤  ≤ 1.
• (^) If  = 1.0, securities perfectly positively correlated
• (^) If  = -1.0, securities perfectly negatively correlated

 p

2 = w 1

2  1

**2

• w 2**

2  2

**2

• 2w 1 w 2**  1,  1  2