Week 7

Question 1

What is the realized sharpe ratio given by?

Answer 1

The average portfolio return - risk free rate/standard deviation of returns. This essentially tells us our return per unit risk. It gives the slope of a straight line that starts from the riskless asset and runs through the portfolio. Investors will typically want to choose a portfolio on this line of steepest slope.
For our active portfolio the return and variance will consist of the benchmark return, benchmark timing, and stock selection) do note that standard deviation is given by sqrt(variance).

Question 2

What does a maximised Sharpe ratio stretch between? What will a client invest in?

Answer 2

The riskless asset and the tangency portfolio, this means the client will invest somewhere on the Tobin frontier based on our risk aversion.
A client will invest somewhere along the Tobin frontier based on their risk aversion.

Question 3

What is the information ratio given by?

Answer 3

The information ratio is a special form of the sharpe ratio, in which only our stock selection components of our active portfolio are left in, as such it is given by:
Alpha of our portfolio divided by the square root of the residual term. It is the Sharpe ratio in active space.

Question 4

What is active space in finance?

Answer 4

Active space records alpha on the vertical axis and standard deviation on the other. Beta must be equal to 1. If beta was not equal to 1 then the residual components would not be the same as the active components.

Question 5

What are ETFs good for?

Answer 5

Lowering stock specific risk, and gaining exposure to something that is difficult or costly to enter directly.

Question 6

What is the Information ratio good for? What will the optimal portfolio do?

Answer 6

It is considered a fundamental fund manager characteristic that measures how good they are. It can be rewritten as alpha = IR* standard deviation of residual/active return. This creates a line through the origin with slope equal to IR, this line is known as a budget constraint, and as a portfolio manager we choose where on this line we wish to invest.
The optimal portfolio will have the highest risk adjusted alpha that crosses this budget constraint slope.

Question 7

Where would we find a passive manager in active space?

Answer 7

The benchmark will be found at the origin of the active space chart, as with no active return or risk and no benchmark timing our portfolio must be the benchmark, this is where we find the passive portfolio manager.

Question 8

What is a pip in currency?

Answer 8

If the currency value is high then a pip starts in the 4th decimal place, however, if the currency is low(like JPY) a pip will start at the 2nd decimal point.

Question 9

How does risk adjusted alpha appear in active space?

Answer 9

Like a parabola, because standard deviation is squared. It will intersect the y-axis at our risk adjusted alpha level, and be made steeper by a larger risk aversion.
A less steep parabola will make the optimal intercept touch the budget constraint higher, making a less risk averse client will lead to a higher risk adjusted alpha value. In the limit where the client is extremely risk averse the risk adjusted alpha will become 0, allowing them to only hold the benchmark.

Question 10

What is a good IR value? What does it very with?

Answer 10

A value of 1 is considered exceptional, meaning 1 percent of return is offset by only 1% extra residual risk. 0.75 is very good, and 0.5 is good, Warren buffet was 0.66.
IR does not vary with aggressiveness, but does vary with time, because returns scale linearly with time, but standard deviation scales with the square root of time.

Question 11

Is alpha a return? What does this mean for calculating portfolio alpha from stock weights and stock alphas?

Answer 11

Alpha is a return. As such the alpha of a portfolio is given by the vector of stock weights transposed * the vector of stock alphas.

Question 12

Why should positive ex post returns be run over a long time horizon?

Answer 12

They could be achieved by change,

Question 13

Why can active returns not be averaged to find the realized return from stock selection if beta does not equal 1? What must we do instead?

Answer 13

Because the returns contain both stock selection and benchmark timing returns. Instead, we must run a regression, where the portfolio return = alpha of the portfolio + beta * benchmark return + error.

Question 14

What is the relationship between a manager’s information ratio and their information coefficient? How do the two components relate?

Answer 14

A manager’s information ratio is approximately equal to: their information coefficient * sqrt (the breadthf of their strategy (how many independent skilled forecasts are made per annum).
Higher skill increases probability of success, while increased breadth allows for better diversification of active bets so that the desired level of overall aggressiveness can increase.

Question 15

What is a manager’s information coefficient?

Answer 15

the correlation of their forecast active returns with realized active returns (correlation of ex ante and ex post alphas).

Question 16

What is a handle in finance?

Answer 16

A handle, refers to the larger numerical part of a financial part of a financial asset price.

Question 17

What does the Black-Litterman formula attempt to do?

Answer 17

Black-Litterman asks us, if we have a variance and risk free rate, and no confidence in the mean returns (due to mean blur). What mean return of stocks would move the Markovitz and Tobin frontiers so that the benchmark portfolio is the tangency portfolio. Essentially, what estimated means returns on a set of stocks forces the benchmark portfolio to be mean-variance efficient.

Question 18

What are the black-Litterman weights given by?

Answer 18

Risk free rate * ones vector + ((benchmark return-risk free rate) over the variance of the benchmark) * the variance matrix * the benchamrk weights.

Question 19

Why can traditional VCV matrices have problems with invertibility?

Answer 19

It needs N*N+1)/2 covariances to be created. It also needs lots of recent data, which will be impossible as we need lots of observations, otherwise we will not have enough degrees of freedom, causing the VCV matrix to not be invertible. When the time series sample is too small, the sample VCV becomes non-invertible, because there are less time series observations than stock counts, if equal it is sometimes invertible, but poorly conditioned. This can lead to some risk asset combinations to falsely appear riskless,(when non-invertible?

Question 20

What is the constant correlation model?

Answer 20

An alternative to traditional VCV. It assumes the covariance of returns on any pair of different stocks is given by the standard deviation of one stock * the other * their correlation. This gives the estimate of covariance to be: (standard deviation estimate(j)* standarad deviation estimate (i) * correlation estimate, if the stocks are different, or the variance if the stocks are the same. The correlation estimate is shared for all pairs of different stocks, meaning this estimated VCV needs only one correlation number and N standard deviation.

Question 21

Why is a mean variance optimizer commonly believed to be wrong? What is the solution?

Answer 21

They tend to overweight stocks with high relative reutrns, negative covariance with other stocks, and low variance of returns, while underweighting stocks with low relative returns, positive covariance of returns with other stocks, and high variance of returns. Howver, these overrepresented stocks tend to have extreme values because of extreme estimation error from sample VCV. By taking an average of the correlation model (lots of specification error but not much statistical estimation error) and the sample VCV( lots of statistical estimation error but not much specification error), the errors will cancel out.
This is commonly done by multiplying both my 0.5 and adding them together.