Part 5. Portfolio Risk and Return: Part I

Question 1

Gross return

Answer 1

The total return on security portfolio before deducting fees for the management and administration of the investment account.

Question 2

Net return

Answer 2

The return after these fees have been deducted, where commissions on trades and other costs that are necessary to generate investment returns are deducted in both gross and net measures.

Question 3

Pre-tax nominal return

Answer 3

This refers to return prior to paying taxes, where dividend income, interest income, ST capital gains, and LT capital gains may all be taxed at different rates.

Question 4

After-tax nominal return

Answer 4

This refers to the return after the tax liability is deducted.

Question 5

Real return

Answer 5

The nominal return adjusted for inflation, measuring the increase in investors purchasing power.

e. g. consider an investor who earns nominal return of 7% over a year when inflation is 2%, the investors approx. real return is simply 7-2 = 5%.
- the investors exact real return is slightly lower, 1.07/1.02 - 1 = 0.049 = 4.9%.

purchasing power:

• if invests $1,000 and earns nominal return of 7%, she will have $1,070 at the end of the year.
• if price of goods she consumes has gone up 2%, from $1.00 to $1.02, she will be able to consumer 1,070/1.02 = 1,049 units.
• she has given up consuming 1,000 units today, but instead able to purchase 1,049 units at end of 1 year, so PP risen by 4.9% = real return.

Question 6

Leverage return

Answer 6

This refers to a return to an investor that is a multiple of the return on underlying asset, calculated as gain or loss on investment as % of investors cash investment.

Investment in a derivative security, such as futures contract, produces leveraged return as cash deposited is only a fraction of value of assets underlying futures contract.

e.g. common in real estate; investors pay for only part cost of property with own cash, and rest of amount is paid for with borrowed money.

Question 7

Money weighted return

Answer 7

The internal rate of return on a portfolio, taking into account all cash inflows and outflows.

The beginning value of account is an inflow, as are all deposits into account, and all withdrawals from account are outflows as the ending value.

Question 8

Time-weighted rate of return

Answer 8

This measures compound growth, the rate at which $1 compounds over a specified performance horizon; the process of averaging a set of values over time.

This is the preferred method of performance measurement, as it is not affected b y the timing of cash inflows and outflows.

Question 9

Things to consider when forming portfolios

Answer 9

• ER and variance return is a simplification as returns do not follow normal distribution, they are negatively skewed, with greater kurtosis (fatter tails) than normal.
• negative skew means tendency to large downside deviations, and positive excess kurtosis reflects frequent extreme deviations on both upside and downside.
• liquidity can affect price and therefore ER of security, a major concern in emerging markets and for securities that trade infrequently, such a low quality corporate bonds.

Question 10

Covariance

Answer 10

This measures the extent to which 2 variables move together over time.

+ve covariance = the variables (e.g. RoR of 2 stocks) tend to move together.

-ve covariance = the two variables tend to move apart/opposite direction.

zero covariance = no linear relationship between 2 variables, so return for next period on one of the assets tells you nothing about return of other asset for the period.

Question 11

How should you interpret the correlation coefficient?

Answer 11

1. CC of +1 - deviations from mean or expected return are always proportional in same direction.
2. CC of -1 - deviations from mean or expected return are always proportional in opposite direction.
3. CC of 0 - there is no linear relationship between stock returns, where in any period knowing actual value of one variable tells you nothing about value of the other.

Question 12

Risk types

Answer 12

Risk averse = the investor dislikes risk (e.g. prefers less risk to more risk), given 2 investments have equal expected returns, they will choose the one with less risk (std dev).

Risk seeking = the investor prefers more risk to less, so given equal expected returns, they will choose more risky investment.

Risk neutral = investor has no preference regarding risk, and would be indifferent between 2 such investments.

Question 13

Minimum variance portfolios

Answer 13

For each level of expected portfolio return, we can vary portfolio weights on individual assets to determine portfolio with least risk, and those with lowest std dev. of all portfolios with given expected return.

THEY TOGETHER MAKE UP MINIMUM-VARIANCE FRONTIER.

Question 14

Efficient frontier

Answer 14

Portfolios that have greatest expected return for each level of risk (standard deviation), coinciding with the top portion of minimum-variance frontier.

Question 15

Global minimum - variance portfolio

Answer 15

The portfolio on efficient frontier that has the least risk.

Question 16

Optimal portfolio

Answer 16

Utility function = of an investor, represents the investors preferences in terms of risk and return (i.e. his degree of risk aversion).

Indifference curve = a tool that plots combinations of risk (standard deviation) and expected return among which an investor is indifferent, assuming these are the only portfolio characteristics investors care about.

Question 17

Risk aversion coefficient

Answer 17

If this value if higher, the more risk averse investor will have a steeper indifference curve.

This is because investor who is relatively more risk averse requires a relatively greater increase in expected return to compensate for given increase in risk.

The slope upward indicates for risk averse investors they will only take more risk (std dev. of returns) if compensated with greater expected returns.

Question 18

2 fund separation theorem

Answer 18

• Supported by combining risky portfolio with risk free asset.
• This theorem states that all investors optimum portfolios will be made up of some combination of optimal portfolio of risky assets and risk free asset.

Capital allocation line = the line representing these possible combinations of risk-free assets and optimal risky asset portfolio.