Portfolio theory and Market Efficiency 5 -7 Flashcards
What is the difference between a population and sample?
A population is the complete set of all items from a system or process that is being studied.
A sample is an observed subset of population values of manageable size.
How do you calculate Expected return ( the amount of profit or loss an investor can anticipate?
Sum of Probability x return according to state of nature. ( basically like the mean)
How do you calculate the sample mean return?
Sum of R data series returns from our sample / N observable observations.
What is the formula for variance ( measures variability from the average or mean.)?
How do you work out the standard deviation ( allows to get to same units ) ?
How do you work out sample variance and sample standard deviation?
What does covariance tell us and what is formula?
measures the direction of the relationship between two variables
What does Correlation tell us and what is the formula?
measure the strength of the linear relationship between two variables ( it scales covariance)
What is the formula for sample covariance?
What is the formula for sample correlation?
sample covariance / product of sample standard deviations
What does this show?
If x and y return a positive covariance/negative: This means that the asset returns generally move together. The returns on assets X and Y are either both below their sample means or both above their sample means.
If x and y return a negative covariance: It means that the asset returns generally move in opposite directions. Where one asset’s
return will be above their sample mean return and the other will be below.
What numbers are correlation inbetween and what if correlation = 1
Correlation = 0 and correlation = -1 ?
Correlation is always a number between -1 and 1 which makes it easier to interpret and is unit free.
Correlation is equal to 1 if there is an exact linear relation with positive slope between X and Y (perfectly positively correlated).
Correlation is equal to 0 if X and Y are uncorrelated
Correlation = -1 means perfectly negatively correlated.
What do portfolio weights and Expected returns mean?
What is the expected return of a portfolio?
How do you work out variance of a portfolio ( KEY) !!! ( N case)
Explain what the double summation means, in exam we are likely to only have 2 assets?
When we have 2 assets, we have 4 terms to add up, if there was 3 there would be 9 terms ygm.
We are going to break down the variance of portfolio equation, so when n = 1 and m = 1, what is the Cov( R1,R1) and what is the Cov ( R1,R2) equal too?
SO Cov(R1,R2) = Cov (R2,R1) so we just need to find 1 and times by 2.
So how can we rewrite to get a more condensed formula for the variance of portfolio?
Here is a visual representation of Variance of a portfolio N asset case, so answer these questions:
1) In a 10 stock portfolio how many terms would need to be added to calculate the portfolio variance?
2) How many of the terms would be variance terms?
3) How many of the terms would be covariance terms?1
4) How many individual covariance terms would you need?
As tend to have a correlation < +1 what is a smart thing to do?>
Have a diversification of portfolio, because it reduces portfolio risk, it averages out the risk. ( variance)
Lets say 2 stocks have a perfect correlation, and the investor is risk adverse, what can he do? plus what does the perfectly correlated line mean?
Moving through the line, changes the weight of the assets in portfolio. If you are risk adverse, you might invest in A because less variance, but the wise thing to do would be to combine stock A and B into a portfolio, as there is a point ( minimum variance portfolio, that gives you the least amount of risk, from these 2 stocks, hence you don’t give up E(R), you get more with less risk.
So when we have 10 assets e.g. in a portfolio and all equal weight, what is the good thing about it, but what is the risk and what shall we think about when investing e.g. say the 11 asset?
The good thing about having 10 assets is that variance decreases, however you cannot diversify away from systematic risk. there are economy wide risk factors that generally result in a positive correlation/covariance between stock terms. So when investing in the 11 asset, its important to not only thing about variance of asset, but how it covaries with the rest of assets in portfolio?>