return, risk and portfolio theory

Question 1

how do we normally measure past performance of a security

Answer 1

by calculating its average return over a historical period

Question 2

what is expected from the variability of stock market returns

Answer 2

an investor considering investing in a stock will face uncertainty about future return on a stock
- a variety of return outcomes are likely to exist, each occurring with a specific probability

Question 3

what is a measure of the risk of a security

Answer 3

the variation around the expected return
- measure of how far the actual return differs from t he expected return

Question 4

how do we derive a quantitative measure of the degree of possible deviations from the expected returns

Answer 4

square root of the variance : standard deviation
- measure of how variable the returns are from the average return
- higher standard deviation = greater variability = higher risk = higher expected return to compensate for it

Question 5

what is a portfolio

Answer 5

a combination of different assets held by an investor

• the share o the value of each individual asset over the total value of= weight of the asset in the portfolio
• sum of the weights of all the assets = one

Question 6

what is the expected return of a portfoio

Answer 6

the weighted average of the expected returns of the individual stocks of which the portfolio is composed of

Question 7

what does calculation of the risk of a portfolio involve

Answer 7

involves correlation of the returns on the 2 stocks
- correlation : measures the degree to which the 2 returns move tgth
- +ve correlation = 2 returns move in the same direction
- -ve correlation = 2 returns move in opposite direction
- 0 correlation = the returns are not related to each other

Question 8

what does the mean-standard deviation frontier show

Answer 8

the expected return and risk that could be achieved by different combinations of the 2 risky assets

efficient frontier: the upper part of the mean-standard frontier and to the right - maximised the expected return for a given standard deviation: section is of interest to risk-averse investors

Question 9

what is the summary of findings for portfolio theory - 2 risky assets:

Answer 9

1. forming portfolios of stocks can substantially reduce risk
2. this result is generated by the lack of perfect correlation between stock returns
3. the lower the correlation, the greater the risk reduction
4. risk-averse investors will tend to prefer ‘diversified’ portfolios

Question 10

what is the feasible region in a mean-standard deviation frontier: N risky assets

Answer 10

set of all points representing portfolios made from N assets
- they are feasible but inefficient portfolios which do not maximise the expected return for a given standard deviation

Question 11

what is the optimal portfolio for an investor who wants to hold a risk-free asset in addition to N risky assets

Answer 11

point where the straight line (optimal capital market line_ is tangential to the risky assets efficient frontier : tangency portfolio

Question 12

what is the effect of increasing securities in a portfolio

Answer 12

the variance (risk) falls as the number of assets held increases
- we can get most of the benefits of diversification with a relatively small number of stocks
- not all risks can be diversified away :
- risk that can be reduced: unsystematic risk (effect of risk only affecting the security)
- risk that cannot be reduced through diversification: systematic risk

Question 13

what are assumptions that underlie the capital asset pricing model theory

Answer 13

1. investors maximise their utility only on the basis of expected portfolio returns and return standard deviation
2. unlimited amounts can be borrowed or loaned at the risk-free rate
3. markets are perfect and frictionless
4. investors have homogenous beliefs regarding future returns - they have the same info and assessment about expected returns, standard deviation and correlation of all feasible portfolios

Question 14

what is the main conclusion of CAPM

Answer 14

in equilibrium, the optimal portfolio of risky assets must be the market portfolio

Question 15

What is the market portfolio

Answer 15

portfolio comprising all assets, where the weight on each asset is the market capitalisation of that asset divided by the total market capitalisation of all risky assets

Question 16

What is the market portfolio

Answer 16

portfolio comprising all assets, where the weight on each asset is the market capitalisation of that asset divided by the total market capitalisation of all risky assets

Question 17

what does the implementation of cAPM require

Answer 17

using proxies for the market portfolio

use of proxies has however led to some academics to argue that CAPM is untestable (cannot analyse data to examine whether CAPM describes what we observe in practise)

Question 18

given that the quality of proxies is poor, what are the 2 alternative outcomes that brings rise to the argument tat it is impossible to test CAPM

Answer 18

1. the market portfolio is efficient (CAPM is valid) but the proxy chosen is poor (empirical tests incorrectly reject the CAPM)
2. proxy of the market portfolio might be good (empirical tests validate the CAPM) but the market portfolio itself is inefficient (validation is fake)

Question 19

what is the relative measure of risk for a security in the CAPM

Answer 19

the correlation between the returns on this security and the returns on the market portfolio

measure is known as Beta: measures the sensitivity of the return on a stock to the return on the market portfolio might

Question 20

what are the characteristics of Beta

Answer 20

ß>1: stock is sensitive to market movements
- such stocks perform better than the market when the market is rising in value but worse when its falling

ß<1: stock is less sensitive
- stocks underperform the market = good stocks to hold when the market is falling

ß = 1 stock mimics the market

Question 21

what does the capital market equilibrium require

Answer 21

the demand for risky assets to be identical to their supply

demand: represented by the optional portfolio chosen by investors
supplY: market portfolio

Question 22

how does the security market line determine whether an asset is over/ underpriced

Answer 22

when capital markets are in equilibrium, all risky securities lie on the SML

when asset is above SML:
- earning excess of return required to compensate for the exposure to market risk
- security is said to be underpriced
- attracts investors = extra demand pushes the stock price and reduce expected return until it sits on SML

under SML:
- overpriced yielding a return below that required to compensate for market risk exposure
- investors sell the asset = drive down the price = raise expected return

Question 23

what are risk seekers

Answer 23

they maximise both risk and return
- theyre willing to accept greater risk for the potential of higher returns by investing including assts such as options, futures, alternative investments and emerging market equities in their portfolio

Question 24

what is a risk neutral investor

Answer 24

they maximise return irrespective of risk
- they will likely pursue a portfolio offering higher returns even if it comes with higher risk

Question 25

what are risk averse investors

Answer 25

they have a low appetite for risk, would rather accept a lower certain return than a substantial risky investment
- prefers a portfolio with a lower certain return than a higher less certain return

Question 26

what is risk tolerance

Answer 26

an amount of risk an investor is willing to take in order to achieve their investment goals and objectives

higher risk tolerance shows a greater willingness to take risk, implying risk tolerance and risk aversions are negatively correlated

Question 27

whys there so much emphasis on the efficient frontier

Answer 27

• portfolios lying on the efficient frontier offer the maximum expected return for their level of variance of return
• efficient portfolios use risk efficiently, investors making portfolio choices in terms of mean return and variance of return can restrict their selections to portfolios lying on the efficient frontier - simplifies their selection process
• if an investor can qualify his risk tolerance in terms of variance or SD of the return, the efficient portfolio for that level of variance will represent the optimal mean-variance choice

Question 28

explain the selection of an optimal portfolio, given an investor’s utility (or risk aversion) and the capital allocation line

Answer 28

when we combine a risk-free assert with a portfolio of risky assets, we create a capital allocation line that we can represent on a graph on the efficient frontier curve. the capital allocation line connects the optimal risky portfolio to the risk-free asset

according to the 2-fund separation theorem, all investors, regardless of risk preference and wealth, will hold a combination of a risk-free asset and an optimal portfolio of risky assets

plotting the risk free asset with the risky portfolio on the graph creates the capital allocation line that

Question 29

what is an indifference curve

Answer 29

plots the combination of risk and return that an investor would accept for a given level of utility

for risk averse investors, IC run northeast since an investor must be compensated with higher returns for increasing risk = has the steepest slope

an investor that is more risk-seeking has an indifference curve that is much flatter as their demand for increased returns as risk increases is much less acute

Question 30

what do expected-returns and standard deviation of returns of a stock tell us about the future return on a stock

Answer 30

the expected return is not the actual return but its an estimate of the actual return based on information about probable return outcomes

the standard deviation of expected returns is an indication of the variability of probable returns around the expected return and hence a measure of risk of the actual return being different from the expected return

Question 31

how is the total portfolio measured and explain how this differs from systematic risk

why is systematic risk a better measure of risk than total portfolio risk

Answer 31

total portfolio risk = portfolio standard deviation

systematic risk = beta of stock or portfolio - measure of how the returns on a stock portfolio co vary with the return on the market portfolio

systematic risk is a better measure of risk as we know that diversification can be used to remove unsystematic risk. so the only risk an investor should be rewarded for is systematic risk

Question 32

what is systematic risk caused by and measured by

Answer 32

interest rates, GDP growth, supply shocks

measured by : covariance of returns with returns on the market portfolio