Topics 1 & 2- Return, Risk and Risk Aversion

Question 1

What is a simple prospect?

Answer 1

• A simple prospect is an investment opportunity with a certain initial wealth and two possible outcomes

Question 2

What does the geometric mean consider?

Answer 2

• considers the principle of

compounding, and we assume that dividend are reinvested

Question 3

Which is always bigger than or equal to, the arithmetic mean or geometric mean?

Answer 3

• Arithmetic mean is always greater than or equal to.

Question 4

What is rule 1 of portfolio math?

Answer 4

Rule 1 : The mean or expected return for an asset is the probability weighted average of its return in all scenarios.

Question 5

What is rule 2 of portfolio math?

Answer 5

Rule 2: The variance of an asset’s return is the expected value of the squared deviations from the expected return.

Question 6

What happens to rules 1 & 2 when assume the probability is equal?

Answer 6

rules 1&2 becomes:
 Arithmetic Mean Return
 S.D.

Question 7

What is rule 3 of portfolio math?

Answer 7

Rule 3: The rate of return on a portfolio is a weighted average of the rates of return of each asset comprising the portfolio, with the portfolio proportions as weights.

Question 8

What is rule 4 of portfolio math?

Answer 8

Rule 4: When a risky asset is combined with a risk-free asset, the portfolio standard deviation equals the risky asset’s standard deviation multiplied by the portfolio proportion invested in the risky asset.

Question 9

What is rule 5 of portfolio math?

Answer 9

Rule 5: When two risky assets with variances
1
2 and 2
2, respectively, are combined into a
portfolio with portfolio weights w1 and w2,
respectively, the portfolio variance is given
by:
p
2 = w1
21
2 + w2
22
2 + 2W1W2 Cov(r1r2)
Cov(r1r2) = Covariance of returns for
Security 1 and Security 2

Question 10

A more positive covariance does what to portfolio variance?

Answer 10

• It increases portfolio variance

Question 11

A more negative covariance does what to portfolio variance?

Answer 11

• It decreases portfolio variance

Question 12

What is a risk averse investor?

Answer 12

• only consider risk free or
  speculative prospects with positive risk premium
• only accept investments
  with positive risk premium (considering both return and risk; A>0)

Question 13

What is a risk neutral investor?

Answer 13

• Don’t care about risk

- judge risky prospects solely by their expected rate of return (considering return only; A=0)

Question 14

What is utility?

Answer 14

• Its a score to rank investment portfolios based on the expected return and risk of portfolios

Question 15

What is a risk seeker?

Answer 15

• Investor that loves risk
• Risk lovers adjust the expected return upward to take into account the ‘fun’ of taking risk (risk becomes positive effect; A<0)