Define gamble

To bet on an uncertain outcome

The assumption of risk for no purpose but the enjoyment of risk

Define speculation

The assumption of considerable risk to obtain commensurate gains

Risk is sufficient to affect the decision

Undertaken in spite of risk involved because one perceives a favorable outcome

Risk aversion and utility : define the axioms of utility

- Comparability (compare and make choices)
- Transitivity (consistency of preferences, eg a preferred to b, b to c, therefore a to c)
- Non-satiety (individual always prefers more to less
- Diminishing marginal utility (the more one has the less each unit adds to utility)
- Certainty equivalence (for every risky choice there is a value (certainty equivalent) that the individual is indifferent between the risky choice and the certainty equivalent)

Utility model, can you add together utiles?

Models are specific to individuals and cannot be added together, inter personal utility comparisons are invalid.

Draw linear, quadratic and logarithmic utility functions

See paper

Define “fair game”

Expected payoff is equal to the cost of the gamble, so expected profit is zero.

Risk averse investor should never accept a fair game

Risk premium

Difference between expected payoff and its certainty equivalent, the cost of risk

Certainty equivalent

The rate that risk free investments would need to offer to provide the same utility score as the risky portfolio.

The rate that, if earned with certainty, would provide a utility score equivalent to that of the portfolio in question.

Risk free asset

Reflects the underlying nature of financial assets (ie return should not be compensation for risk)

Absence of experienced risk (eg variance)

Portfolios of money market instruments are often used as proxies for the risk free asset.

Capital market line (3)

- The strauight line that connects the risk free rate to the optimal risky portfolio
- If a passive investor combines an index portfolio of securities (representing the market) with a risk free proxy, the resulting Capital Allocation Line (CAL) is the Capital Market Line
- CAL = CML if we have the best Sharpe Ratio

Passive investment

Avoids any direct or indirect security analysis

Usually cheaper than active strategies

Free rider benefit, at any time most assets will be fairly priced given that many active knowledgable investors will bid up cheap assets and sell expensive ones

Investment decision

3 steps

- Capital allocation between the risky portfolio and risk free assets
- Asset allocation across broad asset classes
- Security selection of individual assets within each asset class

Capital allocation

Capital allocation determines an investors exposure to risk

Optimal capital allocation is determined by risk aversion as well as expectations for the risk return trade off of the ultimate risky portfolio

Diversification and risk

Extensive diversification cannot eliminate risk. Standard deviation falls but cannot be zero. The risk left after extensive diversification is Market Risk, Systematic Risk, or Non Diversifiable Risk.

Risk that can be diversified is Unique Risk, Firm Specific Risk, Non Systematic Risk or Diversifiable Risk

Expected return

Probabily weighted return in all scenarios

Variance

Expected value of squared deviations from the expected return

Standard deviation

Measure of expected returns around their mean. Square root of the variance

Covariance

How the return on 2 assets moves together

Correlation coefficient

Standardized measure of covariance

When is the power of diversification to reduce portfolio risk unlimited?

When security returns are uncorrelated.

What does irreducible risk of a diversified portfolio depend on

Depends on the covariance of returns of the component securities, which in turn is a function of the importance of the systematic factors in the economy.

When holding a diversified portfolio, contribution of a security will depend on what?

Contribution to portfolio risk of a particular security will depend on the COVARIANCE of that security’s return to those of other securities, and NOT THE SECURITY’s VARIANCE

Markowitz Portfolio Selection Model

- Identify the risk return combinations available from a set of risky assets
- Identify the optimal portfolio of risky assets by finding the portfolio weights that result in the steepest CAL (Capital Allocation Line)
- Choose an appropriate complete portfolio by mixing the risk free asset with the optimal risky portfolio.

What is the minimum variance frontier

Minimum variance frontier is the graph of the lowest possible variance that can be obtained for a given portfolio expected return. Given input data for expected returns, variances and covariances, we can calculate the minimum variance portfolio for an targeted expected return.

Diversifying investments leads to ?? Expected returns and ?? Standard deviations

Higher expected returns and lower standard deviations. Refer to minimum variance frontier

Optimal risky portfolio is identified by?

The optimal risky portfolio is where the Capital Allocation Line is tangent to the efficient frontier. Te CAL dominates all alternatives.

Steps to arrive at complete optimal portfolio (3 steps)

- Specify the return characteristics of all securities (expected returns, variances and covariances
- Establish the risky portfolio (calculate the optimal risky portfolio, then calculate the properties of Portfolio P using weights determined earlier)
- Allocate funds between the risky portfolio and the risk free asset

a) calculate the fraction of the complete portfolio allocated to portfolio P and to Tbills.

b) calculate the share of the complete portfolio invested in each asset and in TBills.

Fair game

expected payoff is the same as the cost to enter the game.

Expected outcome = sum of probability x wealth

* risk averse investor would never accept a fair game, as it has lower utiles.

In the context of certainty equivalent, what is the difference between the expected payoff and the certainty equivalent

risk premium.

Using the quadratic utility model, what is the certainty equivalent

In the quadratic utility function, the certainty equivalent is the same as the utility value since it is the certain return which an investor views as having the same utility as a risky return

Indifference curves

Return - risk combinations that give equal satisfaction

what would a risk averse investor’s indifference curve look like

What does the slope look like if more risk averse?

What does a risk neutral investor’s curve look like

upward sloping.Degree of risk aversion is characterised by the slope of the indifference curve.

If more risk averse, the curve will be steeper

If risk neutral, curve will be horizontal as they do not take risk into account

How can the Capital Allocation Line and the Sharpe Ratio assist in investment decision making

(4 points)

- Diversified fund can be combined with cash to provide the optimal mix
- “Best” diversified fund can be selected from amongst a range of competing products
- Best portfolio will have the highest Sharpe Raio and the steepest sloped CAL (this is the fund manager’s objective)
- CAL also indicates to the fund manager how they might build the optimal portfolio; and deliver a suite of products to meet risk aversion needs of clients

Define market risk

Market risk is the way underlying economic fundamentals impact the market place as a whole

Why is diversification beneficial

Diversification reduces the risks that relate to the specific operations and structure that make a business unique

Minimum variance portfolio

Min variance portfolio has SD smaller than any of the individual component assets

Kintzel Policy Brief - Life Cycle investing -

1. describe approach

2, Describe improvements

Approach to Life Cycle Investing: 1. Determin risk-return needs of client 2. Move along the efficient frontier (minimum risk) 3. Age determines the allocation 4. Array of asset classes not just B + E Could be improved by: 1. Assess appetite for risk 2. Could be influenced by education, circumstances, economic environment