Flashcards in Topics 1 & 2- Return, Risk and Risk Aversion Deck (15)
What is a simple prospect?
- A simple prospect is an investment opportunity with a certain initial wealth and two possible outcomes
What does the geometric mean consider?
- considers the principle of
compounding, and we assume that dividend are reinvested
Which is always bigger than or equal to, the arithmetic mean or geometric mean?
- Arithmetic mean is always greater than or equal to.
What is rule 1 of portfolio math?
Rule 1 : The mean or expected return for an asset is the probability weighted average of its return in all scenarios.
What is rule 2 of portfolio math?
Rule 2: The variance of an asset’s return is the expected value of the squared deviations from the expected return.
What happens to rules 1 & 2 when assume the probability is equal?
rules 1&2 becomes:
Arithmetic Mean Return
What is rule 3 of portfolio math?
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.
What is rule 4 of portfolio math?
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.
What is rule 5 of portfolio math?
Rule 5: When two risky assets with variances
2 and 2
2, respectively, are combined into a
portfolio with portfolio weights w1 and w2,
respectively, the portfolio variance is given
2 = w1
2 + w2
2 + 2W1W2 Cov(r1r2)
Cov(r1r2) = Covariance of returns for
Security 1 and Security 2
A more positive covariance does what to portfolio variance?
- It increases portfolio variance
A more negative covariance does what to portfolio variance?
- It decreases portfolio variance
What is a risk averse investor?
- 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)
What is a risk neutral investor?
- Don't care about risk
- judge risky prospects solely by their expected rate of return (considering return only; A=0)
What is utility?
- Its a score to rank investment portfolios based on the expected return and risk of portfolios