Investment Management
summary
,Week 1: asset allocation and portfolio management
Chapter 5
A few questions to ask when considering an investment in an asset:
- how do you expect index to behave and move? high movement = high risk
- is it worth it? if risk is high, will you have a return?
- how much do you want to invest, if it is worth it?
Holding period of return:
what the return will be
return: how much prices change with respect to some initial price
Not formula sheet!
you look at price change, and possibly dividend over a certain time period
Expected HPR = E[Rit]
what you think return will be
e.g. you expect prices to be either 120 or 90 in time period 1. In period 0 it was 100.
so, investment may gain 20 or lose 10
you also need to know the probability of these price changes. For now, let’s assume both
have equal as big a chance of occurring.
{
1
120→ probability=
2
1
90→ probability=
2
E[R] = ½ x 120 + ½ x 90 = 60 + 45 = 105
Problem: for 2 or 3 price situations this is an easy calculation, but it can occur you have 20+
situations.
Excel solves this: SUMPRODUCT
(random example showing how to operate sum product)
Excess return:
the difference between the return of a risky asset versus the return of a risk-free asset
Not on formula sheet
extra reward for taking risk
Risk premium:
since you do not exactly know what your risky return will be at most points, we need to
calculate it using expected returns
, Not on formula sheet
risk premium is the extra return on top of the risk-free rate you demand for taking the
riskier alternative
RM – RF
Some OIMb reminders:
averages or means are a measurement for the expected return
standard deviation is a measurement for the risk
variance is given on the formula sheet as σ2, std. deviation is just the square root of that
Other statistical measurements:
- skewness characterises the asymmetry of a distribution around its mean
- kurtosis measures the size of a distribution’s tails
important because it matters for significance levels
Sharpe ratio:
looks at the trade-off between risk and return
Formula sheet
risk premium / std. deviation of the excess returns
Std. deviation is not the only measurement of risk:
VaR or Value-at-Risk
quantifies the total risk of a portfolio
Not on formula sheet
way to indicate the probability of a confidence level for which you are sure not to lose
more than X amount of money.
you need a table to calculate the rest, as this is not a mathematical equation
e.g. std. dev. = 20 million, average mean of 0, normally distributed and 99% conf interval.
Excel NORM.INV.N (,99;0;1) = 2,326348
(in which ,99 = 99% conf interval, 0 is average mean and 1 is normal
distribution)
VAR = $20 million x 2.326348 = 46.53
so, with 99% certainty you can say the portfolio is not going to lose more than $46.53
million.
summary
,Week 1: asset allocation and portfolio management
Chapter 5
A few questions to ask when considering an investment in an asset:
- how do you expect index to behave and move? high movement = high risk
- is it worth it? if risk is high, will you have a return?
- how much do you want to invest, if it is worth it?
Holding period of return:
what the return will be
return: how much prices change with respect to some initial price
Not formula sheet!
you look at price change, and possibly dividend over a certain time period
Expected HPR = E[Rit]
what you think return will be
e.g. you expect prices to be either 120 or 90 in time period 1. In period 0 it was 100.
so, investment may gain 20 or lose 10
you also need to know the probability of these price changes. For now, let’s assume both
have equal as big a chance of occurring.
{
1
120→ probability=
2
1
90→ probability=
2
E[R] = ½ x 120 + ½ x 90 = 60 + 45 = 105
Problem: for 2 or 3 price situations this is an easy calculation, but it can occur you have 20+
situations.
Excel solves this: SUMPRODUCT
(random example showing how to operate sum product)
Excess return:
the difference between the return of a risky asset versus the return of a risk-free asset
Not on formula sheet
extra reward for taking risk
Risk premium:
since you do not exactly know what your risky return will be at most points, we need to
calculate it using expected returns
, Not on formula sheet
risk premium is the extra return on top of the risk-free rate you demand for taking the
riskier alternative
RM – RF
Some OIMb reminders:
averages or means are a measurement for the expected return
standard deviation is a measurement for the risk
variance is given on the formula sheet as σ2, std. deviation is just the square root of that
Other statistical measurements:
- skewness characterises the asymmetry of a distribution around its mean
- kurtosis measures the size of a distribution’s tails
important because it matters for significance levels
Sharpe ratio:
looks at the trade-off between risk and return
Formula sheet
risk premium / std. deviation of the excess returns
Std. deviation is not the only measurement of risk:
VaR or Value-at-Risk
quantifies the total risk of a portfolio
Not on formula sheet
way to indicate the probability of a confidence level for which you are sure not to lose
more than X amount of money.
you need a table to calculate the rest, as this is not a mathematical equation
e.g. std. dev. = 20 million, average mean of 0, normally distributed and 99% conf interval.
Excel NORM.INV.N (,99;0;1) = 2,326348
(in which ,99 = 99% conf interval, 0 is average mean and 1 is normal
distribution)
VAR = $20 million x 2.326348 = 46.53
so, with 99% certainty you can say the portfolio is not going to lose more than $46.53
million.
