Samenvatting
Investment Management Summary
Summary of the course Investment Management of the second year of Economics and Business Economics at Radboud University
[Meer zien]Voorbeeld 3 van de 25 pagina's
Voorbeeld 3 van de 25 pagina's
In winkelwagengesponsord bericht van onze partner
Voorbeeld van de inhoud
Summary Investment ManagementChapter 5; risk, return and the historical record
Holding period return (HPR) = realized return; what your return will be, but you cannot be sure about evenutal HPR.
- HPR = dividend yield + capital gain
dividend Pt −P t−1
- HPR = +
Pt −1 Pt−1
- If we want to compare the return of investment with differing horizons, then we need to re-express each
total return as a rate of return over a common period. This is the effective annual rate (EAR);
o EAR = (1 + HPR)1/T – 1
Expected rate of return; what you think your return will be
- E( r)=∑ p( s)r (s)
s
o p(s) = probability of each scenario
o r(s) = HPR in each scenario
Variance (σ2); measure of volatility (wisselvalligheid) and uncertainty
- It measures the dispersion of possible outcomes around the expected value.
- The higher the dispersion, the higher the value of variance, which means more risk, because it is less likely to
observe expected outcome. There thus is more uncertainty.
σ =∑ p(s)¿¿
2
-
s
Standard deviation (σ); measure of risk
- σ =√ σ 2
- A smaller standard deviation means that possible outcomes cluster more tightly around the mean.
The arithmetic average provides an unbiased estimate of the expecte future return.
n n
1
- E( r)=∑ p( s)r (s)= ∑ r ( s)
s =1 n s=1
- E(geometric average) = E(arithmetric average) - ½ σ2
n
1
Estimate variance; σ^ =
2
∑¿¿
n s=1
- Degrees of freedom bias; taking the deviations from the sample arithmetic average instead of taking
deviations from the true expected value.
n
n 1
o Can be eliminated by multiplying σ^ 2 by ¿ ∑
n−1 n−1 s=1
¿¿
- We can improve the accuracy of the estimates of the standard deviation by using more frequent
observations. It is the duration of a sample time series that improves accuracy. Therefore, use the longest
sample that you still believe comes from the same return distribution.
An interest rate is a promised rate of return.
- Nominal interest rate; the growth rate of your money
- Real interest rate; the growth rate of your purchasing power (measured by CPI (consumer price index))
1+ r nom
- 1+r real =
1+ iinflation rate
r −i
- r real = nom
1+i
- Interest rates are determined by;
o The supply of funds by savers
o The demand for funds by businesses and governments
o The expected rate of inflation
,At higher real interest rates, households will choose to postpone some consumption and set aside or invest more of
their disposable income for future use. On the other hand, firms will undertake more projects the lower the real
interest rate on the funds needed to finance those projects. The equilibrium is at the point of intersection.
Government and the CB can shift these curves through fiscal and monetary policies.
The Fisher hypothesis; rnom = rreal + E(i)
- Implies that when real rates are stable, changes in nominal rates ought to predict changes in inflation rates.
- It concerns expected inflation E(i), but we can only observe actual inflation so the empirical validity depends
on how well market participants can predict inflation during their investment horizon.
Risk-free rate; rate you would earn in risk-free assets (such as T-bills)
Risk premium; the difference between the expected HPR and the risk-free rate
- it shows how much of a reward (compensation) is offered for the risk involved in investing in the stock.
- Risk premium = E(r) – rf
Excess return; the difference between the actual return of a risky asset and the return of a risk-free asset.
- Excess return = Ri – rf
The degree to which investors are willing to commit funds to stock depends on their risk aversion.
risk premium E(r p )−r f
Reward-to-volatility ratio = Sharpe Ratio= =
Standard deviations of excess return σp
- The annualized sharpe ratio is obtained when multiplying the sharpe ratio by √ 12
- The higher the Sharpe ratio, the greater the expected return corresponding to any level of volatility.
o Therefore, we seek to maximize the Sharpe ratio by diversifying portfolios.
Normal distribution;
- Is symmetric; the probability of any positive deviation above the mean is the same as a negative deviation.
- Is a well-behaving distribution; which is
stable and additive.
If there is asymmetry, there is skewness;
characterizes the degree of asymmetry of a
distribution around its mean.
Skew= Average ¿
- Skewed to the left (negatively skew); extreme bad outcomes dominate
- Skewed to the right (positively skew); extreme positive outcomes dominate
Kurtosis; the likelihood of extreme values on either side of the mean in the tails (measure of tail risk)
Kurtosis=Average ¿
- High kurtosis means more probability in the tails of the distribution than predicted by normal distribution
Downside risk is an estimation of a security’s potential loss in value if there is a decline in security’s price.
measures of downside risk;
- Value at risk (VaR); the loss corresponding to a very low percentile on the entire return distribution.
o Another name for the quantile q of a distribution; the value below which lie q% of the possible
values (the median is the 50th quantile).
- Expected shortfall (ES) = conditional tail expectations (CTE); measures the expected rate of return
conditional on the portfolio falling below a certain ES value.
- Lower partial standard deviation (LPSD); uses only the negative deviations from the risk-free rate
o Sortino ratio; the ratio of average excess returns to LPSD
- Relative frequency of extreme (3 stdev.) returns; extreme returns are jumps.
Lognormal distribution; the log of the final portfolio value [ln(WT)] is normally distributed.
- By using continuously compounded rates, even long-term returns can be described by the normal
distribution.
, Investments in risky portfolios do not become safer in the long run. On the contrary, the longer a risky investment is
held, the greater the risk. The basis of the argument that stocks are safe in the long run is the fact that the
probability of an investment shortfall becomes smaller. However, probability of shortfall is a poor measure of safety
of an investment because it ignores the magnitude of possible losses.
Chapter 6; capital allocation to risky assets
We expect higher risk-premiums if there is a greater risk. When risk increases with return, the most attractive
portfolio is not obvious. Investors can quantify the rate at which they are willing to trade off return against risk by
assigning utility (welfare) to competing portfolios.
1 2
- U =E(r )− A σ
2
E(r) = expected return
A = index of investor’s risk aversion
σ2 = variance of returns
o Higher utility values are assigned to portfolios with more attractive risk-return profiles (=best).
- Portfolios with the same utility value lie on the indifference curve
o mean-variance criterion; portfolio A dominates portfolio B if
E(rA) ≥ E(rB) and σA ≤ σB
- The investors try to find the complete portfolio on the highest possible indifference curve.
We can interpret the utility score of risky portfolios as a certainty equivalent rate of return; the rate that a risk-free
investment would need to offer to provide the same utility as the risky portfolio.
- Accept portfolio (invest in risky portfolio) if certainty equivalent > risk-free rate
- Reject portfolio (invest in risk-free portfolio) if certainty equivalen < risk-free
rate
The amount of risk-aversion can be determined by using observations or a
questionnaire.
- Risk-neutral investors (A = 0) judge risky prospects solely by their expected
rates of return.
o The portfolio’s certainty equivalent rate is simply the expected rate of
return.
- Risk lover investors (A < 0) engages in fair games and gambles
o Adjusts expected returns upwards due to the ‘fun’ of taking risks
- Risk-averse investors (A > 0)
More risk-averse investors have steeper indifference curves, which means that investors require a greater increase
in expected return to compensate for an increase in portfolio risk (higher Sharpe Ratio).
Capital allocation; the proportion (y) of your complete portfolio to invest in risky or risk-free assets.
Complete portfolio; the combination of a risky asset portfolio (rp) and the risk-free asset (rf)
- Return on complete portfolio rc = yrp + (1 – y)rf
- Standard deviation of the complete portfolio σC = yσp , since the stdev. of risk-free asset is zero.
The Capital Allocation Line (CAL) graphs all the available risk-return combinations.
rise E (r p )−r f risk premium
- Its slope is the Sharpe Ratio; S= = =
run σp σp
- Its intercept is the return on the risk-free asset.
E( r p)−r f
o E( r ¿¿ c)=r f + ∙ σc ¿
σp
- It shows the investment opportunity set; the set of feasible expected return and
standard deviation pairs of all portfolios resulting from different values of y
(proportion in risky asset).
o Investors choose the allocation to the risky asset (y) that maximizes their
utility function
1 E( r p)−r f
U =E(r )− A σ 2 and E( r ¿¿ c)=r f + ∙ σc ¿
2 σp
Voordelen van het kopen van samenvattingen bij Stuvia op een rij:
Verzekerd van kwaliteit door reviews
Stuvia-klanten hebben meer dan 700.000 samenvattingen beoordeeld. Zo weet je zeker dat je de beste documenten koopt!
Snel en makkelijk kopen
Je betaalt supersnel en eenmalig met iDeal, creditcard of Stuvia-tegoed voor de samenvatting. Zonder lidmaatschap.
Focus op de essentie
Samenvattingen worden geschreven voor en door anderen. Daarom zijn de samenvattingen altijd betrouwbaar en actueel. Zo kom je snel tot de kern!
Veelgestelde vragen
Wat krijg ik als ik dit document koop?
Je krijgt een PDF, die direct beschikbaar is na je aankoop. Het gekochte document is altijd, overal en oneindig toegankelijk via je profiel.
Tevredenheidsgarantie: hoe werkt dat?
Onze tevredenheidsgarantie zorgt ervoor dat je altijd een studiedocument vindt dat goed bij je past. Je vult een formulier in en onze klantenservice regelt de rest.
Van wie koop ik deze samenvatting?
Stuvia is een marktplaats, je koop dit document dus niet van ons, maar van verkoper T00. Stuvia faciliteert de betaling aan de verkoper.
Zit ik meteen vast aan een abonnement?
Nee, je koopt alleen deze samenvatting voor €6,99. Je zit daarna nergens aan vast.
Is Stuvia te vertrouwen?
4,6 sterren op Google & Trustpilot (+1000 reviews)
Afgelopen 30 dagen zijn er 53340 samenvattingen verkocht
Opgericht in 2010, al 14 jaar dé plek om samenvattingen te kopen