Chapter 5 - Risk and Returns Flashcards
What is the mode?
- most frequent number in a set
what is the median?
- the number in the middle of the data set when they are organised in size order
What is the mean?
- more mathematically accurate average
- it involves adding up all the numbers and dividing this number by the amount in that data set
how to calculate weighted probability
- multiply each annual return by the probability
what is a normal distribution?
- It means that most of the examples in a
set of data are close to the ‘average’,
whilst relatively few examples tend to
be at one extreme or the other.
what is standard deviation?
measures how widely the actual return on an investment varies around its average or mean return
the greater the standard deviation, the more it varies from its average return
calculation for standard deviation
standard deviation (σ) = √𝒗𝒂𝒓𝒊𝒂𝒏𝒄𝒆,
standard deviation percentages
o 68% of outcomes will be within 1 standard deviation of the mean
o 95% of outcomes will be within 2 standard deviations of the mean
o 99%+ of outcomes will be within 3 standard deviation of the mean
what is beta?
measure of volatility; how much its price varies. The more volatile a share price, the more risk for investors
An assets beta will show the extent to which that asset moves in line with changes in the market
what is positive correlation?
Positive correlation
•is where profits and share values move in the same general direction as each other in
response to market changes because they are influenced by the same things.
what is negative correlation?
•is where the profits of companies move in opposite directions in response to market
changes.
•A good example would be a wellington boot company and a sun-cream manufacturer.
•They are in different, almost opposite, markets and they face different seasonal
challenges, so their fortunes will vary opposite to each other.
what is no correlation?
•is where the profit and the shares of companies have no relationship to each other at all.
•They are affected by completely different things and are unlikely to show any similarities to or differences from each other.
what is the efficient frontier?
The efficient frontier uses a portfolio’s standard deviation to measure the risk, and plots the risk-reward profiles of various portfolios on a graph and shows the best return that can be expected for any given level
of risk.
what info do you need to plot an efficient frontier curve?
• the return of each asset
• the standard deviation of each asset’s return
• the correlation between the asset’s returns
limitations of efficient frontier
• It assumes that investment returns follow a ‘normal distribution’ pattern, and that standard deviation is
the correct measure of risk.
• For some investors, ‘attitude to risk’ may not be their only or key consideration. For example, they may
have ethical preferences that mean some portfolios are unacceptable to them.
• It works on historic data and, as we know, past performance is no guide to future performance.
• The model takes no account of charges within the investments.
• It is difficult to get sufficient data to plot the graph.
what is modern portfolio theory
Modern Portfolio Theory considers the way portfolios of investments can be structured to maximise returns and minimise risks.
It argues, reasonably, that investors are fundamentally risk-averse.
Markowitz demonstrated that portfolio diversification could reduce risk and increase
returns for investors.
He concluded that ‘The best-diversified portfolio was of imperfectly correlated asset classes’.
What is CAPM
CAPM states that ‘in order to consider a risky asset, an investor would want a return that equals the risk-free return plus, as a form of compensation, an additional return that takes account of the risks taken’.
To calculate it:
Return - risk free return
Times this by the BETA
Add risk free return back to it
CAPM Assumptions
1) Investors are rational and risk averse
2) All investors have an identical holding period
3) There are many buyers and sellers
4) No taxes, costs or short selling restrictions apply
5) All information is available, liquidity can be ignored
6) Investors can borrow money at risk free rates
7) Investors make decision on basis of risk and return alone
CAPM Limitations
1) finding risk free rate is difficult
2) choosing market portfolio is sometimes easier said than done
3) Beta must be assumed to be stable
Benefits of using CAPM
• Easy to calculate, uses widely available information.
• Takes account of systematic / market risk.
• Reflects the fact that most portfolios are diversified to remove unsystematic risk.
• It is a robust and trusted calculation.
• It can give an expected return / benchmark.
what is fama and french
• Expands the CAPM model.
• Adds-in factors for company size and value, in addition to the market risk.
• They discovered that small companies tend to outperform larger ones.
• However smaller companies are more volatile.
what is arbitrage pricing theory
• Developed by Stephen Ross.
• Arbitrage is the process of taking advantage of a security’s mispricing to make a
risk-free profit.
• The theory states that a security’s return can be predicted using the
relationship between it and a number of common risk factors.
• APT is based on the belief that asset prices are determined by more than just
one type of market risk.
• APT states that the expected return is determined by adding the risk-free rate
to figures for each different risk factor.
What is weak form efficiency
- This states that the current share price fully reflects all past price and trading information and that future prices cannot be predicted by analysing historical data.
•So, any technical analysis of company information is meaningless as it has no bearing on the future.
what is semi-strong efficiency
•This states that share prices adjust to all publicly-available information, very rapidly and in an unbiased way.
•So, investors cannot benefit from the information to gain excess returns above the market.
•It perceives public information to be all past trading information, company accounts and other economic factors.
•Again, analysis of the information looking for clues is meaningless. It’s already been done and the price seen reflects that.
what is strong form efficiency
•If you believe in strong form you would believe that the share price seen not only reflects public information but also all private information held by a firm’s directors.
•Remember; insider-dealing, the trading of stock based on information that is not in the public
domain, is illegal.
what is loss-aversion
- Loss aversion is the idea that people are more concerned with losses than gains of the same magnitude.
- The pain of losing is often psychologically twice as strong as the pleasure of gaining.
People are more likely to take risks to avoid a loss than to make a gain. - Loss aversion is a key part of prospect theory, a model of decision-making under risk and uncertainty.
What is hindsight bias?
• The investment world is never short of people who can give detailed reasons for
an event after it has happened.
• The ease with which such explanations emerge – whether or not they are correct
– can lead to investors believing that the sequence of events was obvious and
that their investment advisers have let them down.
what is regret?
• As mentioned in loss-aversion, investors tend to ‘hang on in there’ when faced
with a loss, even when it would be prudent to cut their losses. It is almost a case
of not wanting to admit a mistake has been made.
• By not selling, they can avoid regretting their purchase
what is anchoring?
• Investors often ‘anchor’ on numbers they know. If they paid a certain price for a
company’s shares, then they tend to think that anything less is cheap and
anything higher is expensive, regardless of the fortunes of the company.
• A similar fixation can occur with round numbers such as ‘crossing the 7000
threshold’ on the FTSE 100 index.
what is over confidence?
• Investors overestimate their own skills and underestimate the likelihood of bad
outcomes.
• Too much emphasis is placed on past performance and recent trends.
• This leads people to believe that they are better at calling the market or stock
picking than they actually are.
• Selective memory can also reinforce this, remembering the good bets but
forgetting the bad ones
what is mental accounting?
• Investors often compartmentalise money, having separate pots for different
objectives.
• The same can happen with investment returns, such as only spending the income
and not their capital. But as some investments take the charges from capital
then this can lead to spending come of the capital each year.
• It is best to consider total returns and not overemphasise the relevance of its
components.
what is herding?
• Investors tend to follow the crowd rather than good advice or research. This
really is FOMO (fear of missing out) at work.
what is endowment effect?
• Investors tend to value stocks simply because they own them and have an
aversion to losing them.
• It explains why individuals who inherit investments tend to retain them without
any changes, even though they are unlikely to meet their risk profile or capacity
for loss.
what does it mean to measure performance?
- This looks at the mathematical return achieved
what does it mean to evaluate performance?
- This looks at how the performance compares to something else
what is performance attribution?
- This looks at how results were achieved
Future value formula
PV(1+r)n
Regular Savings formula
(1+r)n - 1
/
r
x by present value
What is the MWR and TWR used for
• MWRs can be used to calculate a valid return for an individual portfolio, but it gives misleading results if it is used for comparative purposes.
• TWRs are widely used for comparative purposes because they are not affected by the timing of cash flows and new money inflows.
What is the sharpe ratio?
- A measure of risk adjusted returns
- Compares active funds against each other
- Only useful when comparing funds with similar objectives
Formula is:
Return - risk free return / standard deviation
The greater the sharpe ratio it’s better it’s risk adjusted return has been
what is the information ratio?
- evaluates portfolios performance relative to performance of a benchmark
- often used to compare funds against tracker
- can be misleading if returns are not normally distributed
formula is:
return - benchmark return / tracking error
- useful to gauge skill of fund managers, and shows the consistency with which a manager beats a benchmark index
- negative information ratio shows would have been better in a tracker fund
what is alpha?
- looks at the actual growth achieved by a portfolio compared to what we would have expected it to be
- measures stock picking skills of a manager
- positive alpha indicates good stock selection
Formula is =
actual portfolio return - CAPM expected return
state two benefits and two drawbacks of using sharpe ratio
Benefits
• Sharpe ratio can be used to compare different funds or managers.
• It shows the risk-adjusted returns, looking at extra you are getting back per unit of risk.
• It can identify if returns are from excess risk or good management of the fund through effective stock-picking.
Drawbacks
• Shouldn’t be used in isolation as need to consider other factors and look at ratios as a trend over time.
• Ratios using standard deviation as a measure of risk, assume that the returns follow a normal distribution curve.
• It doesn’t take into account costs of trading.
