return, risk and portfolio theory Flashcards
how do we normally measure past performance of a security
by calculating its average return over a historical period
what is expected from the variability of stock market returns
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
what is a measure of the risk of a security
the variation around the expected return
- measure of how far the actual return differs from t he expected return
how do we derive a quantitative measure of the degree of possible deviations from the expected returns
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
what is a portfolio
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
what is the expected return of a portfoio
the weighted average of the expected returns of the individual stocks of which the portfolio is composed of
what does calculation of the risk of a portfolio involve
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
what does the mean-standard deviation frontier show
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
what is the summary of findings for portfolio theory - 2 risky assets:
- forming portfolios of stocks can substantially reduce risk
- this result is generated by the lack of perfect correlation between stock returns
- the lower the correlation, the greater the risk reduction
- risk-averse investors will tend to prefer ‘diversified’ portfolios
what is the feasible region in a mean-standard deviation frontier: N risky assets
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
what is the optimal portfolio for an investor who wants to hold a risk-free asset in addition to N risky assets
point where the straight line (optimal capital market line_ is tangential to the risky assets efficient frontier : tangency portfolio
what is the effect of increasing securities in a portfolio
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
what are assumptions that underlie the capital asset pricing model theory
- investors maximise their utility only on the basis of expected portfolio returns and return standard deviation
- unlimited amounts can be borrowed or loaned at the risk-free rate
- markets are perfect and frictionless
- 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
what is the main conclusion of CAPM
in equilibrium, the optimal portfolio of risky assets must be the market portfolio
What is the market portfolio
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
What is the market portfolio
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
what does the implementation of cAPM require
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)
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
- the market portfolio is efficient (CAPM is valid) but the proxy chosen is poor (empirical tests incorrectly reject the CAPM)
- proxy of the market portfolio might be good (empirical tests validate the CAPM) but the market portfolio itself is inefficient (validation is fake)
what is the relative measure of risk for a security in the CAPM
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
what are the characteristics of Beta
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
what does the capital market equilibrium require
the demand for risky assets to be identical to their supply
demand: represented by the optional portfolio chosen by investors
supplY: market portfolio
how does the security market line determine whether an asset is over/ underpriced
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
what are risk seekers
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
what is a risk neutral investor
they maximise return irrespective of risk
- they will likely pursue a portfolio offering higher returns even if it comes with higher risk
what are risk averse investors
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
what is risk tolerance
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
whys there so much emphasis on the efficient frontier
- 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
explain the selection of an optimal portfolio, given an investor’s utility (or risk aversion) and the capital allocation line
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
what is an indifference curve
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
what do expected-returns and standard deviation of returns of a stock tell us about the future return on a stock
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
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
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
what is systematic risk caused by and measured by
interest rates, GDP growth, supply shocks
measured by : covariance of returns with returns on the market portfolio
