week 3

Question 1

How do we calculate the minimum variance portfolio returns

Answer 1

step 2: standardise

Sign next to s is a matrix 1, so multiply var cov with 1 vector

Question 2

What is a easy mistake you can make with the sharpe ratio

Hint: T

Answer 2

Sharpe is commonly denoted on an annual basis whilst our data is monthly
Anualized return - anualized rf / Sqrt(12)* stdev

Question 3

What are the steps to calculate the efficient portfolio with short sale constraints

Answer 3

1. choose some random values for weights
2. make sure to have a total of 100%
3. Calc portfolio statistics including sharpe
4. open solver “max” sharpe by including constraints

Question 4

What are the steps to calculate the market-capitalization-weighted “market” portfolio

Answer 4

1. calculate the weights by use of the market cap
2. make sure to have a total of 100%
3. Calc portfolio statistics

Question 5

Write down four reasons why in practice investors buy the mcap-weighted market proxy instead of the optimal market portfolio

Answer 5

1. expected returns are based on historical returns and those are not good predictors of the future.
2. The variance covariance may contain estimation uncertainty. Its not complete crap but still in some market scenarios. Some expected diversifiers might not be anymore in the future
3. Transaction costs and turnover is high, its difficult to montain. Every month will change the optimal weights, rebalancing. Market cap adjusts automatically. Market cap * price.
4. Takes more effort. The management fee is higher.

Question 6

What are the steps in the black-litterman model

Answer 6

Question 7

Step 2 BL: Calculate the expected returns that are implied by the mcap-weighted portfolio

Answer 7

Question 8

Step 3 BL: Incorporate our opinion of the expected market return

Answer 8

output is the factor

Our opinions are always in excess of rf / variance of market.

Question 9

Step 4 BL: Re-calculate expected returns with normalization
*also give the check you do here

Answer 9

Var cov * marketweights * normalisation + rf
Check: mmult weights * new implied returns = your opinion

Question 10

Step 5 BL: incorporate our stock opinions

Answer 10

We use the covariance matrix which makes elegant. (opinion on one stock impacts other stocks)
formula:
Market implied return + (small component that depends on the covariance of the stock we’re adjusting with stock we have opinion about / stock we have opinion about) * opinion

always fix opinion and denominator (variances)

Question 11

Step 6: Calculate opinion-adjusted optimal portfolio

Answer 11

Look a lot like market portfolio but with adjusted er

Question 12

RBSA step by step

Answer 12

1. make a returns row with portfolio returns, replication and error row next to the building block row. Add a weights row above the building blocks
2. Replication formula: sumproduct(buildingblocks, weight row), error formula= portfolio-replication)
3. make an error variance, total weights and r2 cell
4. use solver objective; min error variance with the weights row. Add constraints

Question 13

What is the result of the black jensen scholes research?

Answer 13

The SML is too flat. On average, portfolios with a low beta have historically had positive alpha’s and for alpha’s its the other way around.

Question 14

How does the compensation work for portfolio managers of hedge funds and mutual funds?

Answer 14

Compensation of manager depends on performance
* Hedge funds: incentive fee based on realized fund return
* Mutual funds: good performance increases AUM, which increases compensation for fund manager

Question 15

How can a manager inflate performance measures? What is “manipulation”

Answer 15

1. Smoothing returns
2. Non-linear strategies, e.g., writing put options
3. Deviating from proclaimed investment style (style drift)

Manipulation is action to increase a fund’s performance
measure that does not actually add value for investors

Question 16

What is return smoothing? How does it affect performance measures

Answer 16

Practice of delaying reporting of true returns to create impression
that fund is less risky than it really is (reduce volatility)
* In very good months, report smaller profits than actually realized
* In very bad months, report smaller losses than actually realized

How does smoothing affect performance measures?
* Std. dev. of reported returns too low  Sharpe, Sortino, and IR overstated
* Correlation of reported returns with factors (and hence betas) biased
towards zero  alpha, TR, and IR overstated if factor premiums are +

Question 17

Why does positive autocorrelation in fund returns may suggest smoothing

Answer 17

Autocorrelation in the context of finance refers to the relationship between a financial time series data and its lagged values (values from previous periods). Positive autocorrelation means that the values of a variable (such as fund returns) tend to be positively correlated with their own past values at specific time lags.
When discussing fund returns, positive autocorrelation might suggest a practice known as “smoothing.” Smoothing refers to the deliberate manipulation of reported returns to present a more stable or consistent performance pattern over time. This can be achieved by fund managers to portray a more favorable picture of the fund’s performance, often for marketing or investor retention purposes.

Question 18

What is market timing?

Answer 18

Market timing involves shifting funds between marketindex
portfolio and safe asset
* Increase exposure to market when market return is higher, lower exposure in bad times -> non-linear relation between portfolio return and market return

Question 19

What are the pro’s and cons of return based style analysis?

Answer 19

Pros
* Can handle any strategy for which passive indexes exist
* Simple: uses only return information (no holdings needed)
* Powerful: can detect if fund deviates from declared style
* Gives insights on how to replicate fund’s return -> reverse engineer investment strategies using only historical performance data
Cons
* Depends on appropriate selection of benchmarks
* Not immune to some forms of manipulation (e.g., return smoothing)
* Statistical testing difficult if benchmarks are strongly correlated
* Yields average style, does not capture rapid style changes