Week 6

Question 1

What is our active return? What is our active risk? Active beta? What is the rule

Answer 1

The return of our managed portfolio minus the return of our benchmark, the active risk is the variance of our (active return - our benchmark return), the active beta is our managed beta - our benchmark beta (which will be our portfolio beta - 1).
The rule is that active = portfolio - benchmark, and even applies to portfolio weights.

Question 2

Are quantitative or qualitative strategies better over the long term?

Answer 2

They are neck and neck, with the lead constantly changing.

Question 3

What is the difference between fundamental and quantitative managers?

Answer 3

Fundamental managers have a team of analysts, they investigate financial statements, physically visit and phone companies to talk about earnings, ask what and why the company is doing things, figure out the expected earnings, and value companies and forecast future earnings.
Quantitative managers, have very few analysts, instead they use signals driven by quantifiable variables, using a computer rather than visiting the company. They typically rank companies and tilt their portfolio weights towards the most attractive and away from the least, rather than valuing the companies implicitly.

Question 4

Why is Benjamin Graham’s quantitative approach similar to many fundamental approaches? How is the Grinold-Kahn approach different? What are their relative numbers of stocks in the portfolio

Answer 4

His quantitative approach uses equity screens as binary hurdles, to either stop or allow companies into the portfolio. This means there will only be 10-30 stocks in a portfolio.
The Grinold-Kahn quantitative approach is more about weights, meaning they will have the same number of stocks as the benchmark, but with different weights.

Question 5

What are realized alphas? What is the argument for using a mix of fundamental and quantitative managers relating to this?

Answer 5

The returns over and above the returns associated with exposure to benchmark risk. The correlation between fundamental and quantitative manager alphas is roughly 0. This means we can reduce our short-term risk without damaing long-term returns as long-term performance is similar.

Question 6

What is a marketable share order? What is a marketable limit order?

Answer 6

A marketable share order is one for which an opposing order is sitting in the book which it can be crossed with. It will be executed immediately. A limit order that is immediately marketable is called a marketable limit order.

Question 7

Are passive and active investing terms interchangable?

Answer 7

In a lot of cases yes, they are only used unambiguously at the extremes.

Question 8

What can active investment in equities be broken into?

Answer 8

stock selection and benchmark timing.

Question 9

What is benchmark timing? What is it essentially a bet on?

Answer 9

In benchmark timing we use skilled forecasts of returns to the benchmark to time aggressive and defensive moves (seeking beta not equal to 1 for a time period), this could be done by using high-beta or low-beta stocks, or possibly ETFs, options, or futures. If we do not wish to time the market we must ensure our portfolio beta is equal to 1.
It is essentially a bet on a single asset, the portfolio of stocks underlying the benchmark.

Question 10

What is stock selection in terms of active investing?

Answer 10

Stock selection uses forecasts of stock returns, usually for a portfolio, in an attempt to outperform a benchmark. These forecasts must be different from the market consensus (Which typically comes from CAPM or a related model) if they are to lead to active positions.

Question 11

Is the size of a market correlated with its efficiency?

Answer 11

Yes, larger markets are typically more efficient than smaller markets.

Question 12

Does active management involve ex-ante or ex-post returns? What is maximised?

Answer 12

It uses forecasts of returns, so ex-ante. They aim to maximize a utility function, parameterized via the level of client risk aversion.

Question 13

What is a good portfolio to use as our market portfolio?

Answer 13

Some well specified benchmark like the S&P500/

Question 14

What are the steps to generating skilled forecasts of stock returns?

Answer 14

1. Identify quantifiable characteristics of stocks that are associated with outperformance (there are many).
2. Collect measures of these characteristics and run them through some standardizing transformations so they are not overwhelmed by other components.
3. Run a backtest to see whether these characteristics add value after transaction costs.

Question 15

Why is it not fair to compare our portfolio of overperformant stocks to any benchmark?

Answer 15

Some of the characteristics of overperformance can be thought of as driving alpha and beta risk. As such, comparing to a benchmark that is not subject to the same stock features is not fair as the level of risk will be different.

Question 16

Can we take the alpha of a stock within our portfolio, relative to our portfolio? Why might this be useful?

Answer 16

Yes, we can attempt to increase the weights of the higher alpha stocks and lower the weights in negative alpha stocks.

Question 17

What is strategic asset allocation? What about tactical asset allocation?
What are they known as when combined?

Answer 17

Also known as “core” investing, this is the long-term choice of beta risk made by high level decision makers.
Tactical asset allocation (also known as “satellite” investing) is the short-term choice of alpha/tilt exposure made by day-to-day portfolio management staff.
When combined these are known as “core-satellite” investing.

Question 18

What do smart-beta advocates suggest?

Answer 18

That investors should focus on how they allocate money to the different risk factors that drive returns.

Question 19

What is the standard client utility function made of?

What is the benefit of the traditional CAPM objective function that comes from this?

Answer 19

Most investors want more returns and less risk, as such, utility is often a positive function of expected return and a negative function of risk.
This creates an objective function (traditional CAPM-type mean/variance): utility = expected return - risk free rate - (client risk aversion * portfolio variance).
The risk aversion will vary based on the client, but this funcitonallows us to put variance and returns over the risk free rate on equal terms.

Question 20

What is a skilled forecast? What does this mean for our objective function with active management?

Answer 20

one which is different from a naive CAPM-type consensus forecast.
For active management this makes our objective function: skilled forecast predicted return - risk free rate - (client risk aversion * variance of portfolio).

Question 21

Why is having only one measure of risk aversion for the client bad?

Answer 21

Clients may have multiple types of risk aversion, for example, being more afraid of unreliable alphas(active risk) and fees than the risk from the benchmark itself. This can mean that maximizing the total-return-risk objective function will cause the fund to take on too much active risk for possibly two reasons.

1. The active risk in a conservative active fund is a small slice of the total risk.
2. The client’s aversion to active risk is higher than the client’s aversion to benchmark risk or total risk, causing the risk aversion coefficient on total risk to have difficulty suppressing the active risk.

Question 22

What is the return of a stock/portfolio given by relative to benchmark and residual return?

Answer 22

risk free rate + beta*(benchmark return - risk free rate) + the residual return of the stock after accounting for the benchmark return.
The residual return is given by the skilled estimate of the return above the consensus estimate (alpha) + an error value (which is expected to be 0 for both the consensus and skilled estimate).

Question 23

What allows skilled traders to beat the Markowitz approach?

Answer 23

A skilled trader is believed to be able to see the alpha of a stock, while unskilled traders cannot, this allows them to beat the Markowitz approach as in this case all traders are assumed to have the same information.

Question 24

What is the relative spread of bid and ask prices like over the day? What does this mean if we want to predict the mid day spread?

Answer 24

higher at the beginning of the day (price is uncertain), and end of the day (people want no open positions), than in the middle of the day by about double. As such we can approximate the mid day spread as half the closing spread.

Question 25

What is the second moment of active returns given by when the benchamrk and residual return are statistically independent? (The variance) What occurs when the portfolio examined is the benchmark?
Why is this the same for a skilled and unskilled investor?

Answer 25

The (variance of the benchmark portfolio + the beta of the managed portfolio squared - 1)*the variance of the benchmark portfolio + the variance of the residual return.
If the portfolio is the benchmark then there will be no benchmark timing, or stock selection.
There is no alpha term so the variance decomposition is the same for a skilled and unskilled investor, meaning only the first moment of returns can be forecast.

Question 26

What is active return given by? What is the residual return given by and what is the difference? Why is this useful?

Answer 26

(Beta of the portfolio - 1)*(return of benchmark-risk free rate) + residual return.
Residual return is given by the (portfolio return - risk free rate) - beta of the portfolio * (return of benchmark-risk free rate). The residual return is the active return with the beta effect removed. This means the active return ans residual return when the beta is 1. This also applies to active risk and residual risk.
This allows us to use the two terms interchangably when there is no benchmark timing (as beta = 1).

Question 27

What is the full return of our skilled portfolio given by? What are the parts? Do the same for risk of the skilled portfolio

Answer 27

benchmark return + (benchmark timing, (beta of portfolio - 1) * return of benchmark + deviation of skilled forecast from benchmark)) + stock selection (alpha of portfolio, the residual term).
The risk of the skilled portfolio equals the benchmark risk + (benchmark timing, ( beta^2 - 1)*variance of the benchmark) + stock selection (the residual risk).

Question 28

What can we do if we break down our active return and active risk components? What two components can we drop?

Answer 28

We can multiply each return component by its associated risk component, and then add them together. This allows us to generate an objective function which we can use to give our clients different potential risk aversions. Often we can drop the components that come from the benchmark as they have no relation to our stock weights, as our choice variable(stock weights) is not related to this it will not change our optimization.
We also typically remove benchmark timing, making beta = 1, this leaves only the residual return and its risk as associated with stock selection.

Question 29

Why will the argmin of an equation like x^2 be the same as x^2 + 7

Answer 29

The +7 does not carry over on differentiation.

Question 30

What is our final equation for risk adjusted alpha including transaction costs? When do transaction costs occur, as such how can we approximate them?

Answer 30

RTAA = alpha of portfolio - (total risk aversion * variance of residual return) - transaction costs. Transaction costs only occur due to a change in position, as such they are given by:

How often we intend to change per annum * change * halfspread.
The change is the absolute value of (new weights - old weights), and halfspread is 0.5*vector of estimated middle-of-the-day relative bid-ask spreads.

Question 31

What cost do we pay if we demand liquidity and buy at the ask price? What about if we demand liquidity and sell at the bid price?

Answer 31

If we demand liquidity and buy at the ask price we will have to pay a half-spread above fair value, if we demand liquidity and sell at the bid price we will receive a half-spread less than fair value.

Question 32

What is the sharpe ratio given by?

Answer 32

The average difference of returns between two assets/ the standard deviation of returns.