Resampled Efficient Frontier

CFA Level III Portfolio Management
#1

Can someone please explain to me resampled efficient frontier in simple English.

#2

I’m not a PM but this is how I think about it simply.

You have a bunch of assets you can invest in from. You want to come up with the best combination of assets that will generate your efficient frontier. You come up with what you think is the expected return of each asset and looking at historical vol, you plot these guys and that’s your efficient frontier. But all you’ve really done is provide a single point estimate. What are the chances that of all the possible efficient frontiers out there, you chose/calculated the exact curve?

So instead what you do is you run some Monte Carlos. Let’s just focus on 1 asset to make it easy. You think stock ABC will return 10% in the future and based on historical vol, you realize 1 standard deviation is +/- 5%, so there’s a 67% chance the return can actually be 5 to 15%.

So what the Monte Carlo will do is run 10,000 random simulations based on the parameters you layed out (an expected mean return of 10% and 1 standard deviation of +/-5%). The 10,000 paths generated will fit a normal curve. So in essence, instead of providing a single estimate, stock ABC is going to return 10%, you show a bel curve or distribution of expected returns where the middle is 10%.

Now think of this large scale for all assets, and you also throw in correlation, covariances, etc with each asset. But instead of the output being the individual return of assets, you show the efficient frontiers instead. The original efficient frontier you forecasted is in the middle. The other 9,999 are to the left and right, but it shows up “blurry”.

If I had to relate back to my single asset example, it’s the difference of 1 guy telling you stock ABC is worth $32, and another guy saying $32 with a 1 standard deviation ranging from $24 to $40. But instead of stock prices, you’re doing this for efficient frontiers.

#3

Simple English: generates a multiple distribution of portfolios at each level of risk (instead of 1 for MVO).

Strengths: more diversified, more stable (lower transaction costs)

Weakness: no statitistical rationale

Thats what I have in my notes.

#4

Correcting a (small) detail in Jmachine4 statement: it lacks ECONOMIC THEORY rationale (there is a statistical rationale…)

#5

Thanks Guys.

#6

not quite sure that I follow the entire rationale of resampled EF, but this is the best explanation I’ve seen so far.

#7

I’ll give it a shot:

Suppose that you create the efficient frontier by using historical returns, volatilities of returns, and correlations of returns. You may fiddle with them a bit, but, in any case, you choose a single number for each return, each volatility, and each correlation (or covariance).

That gives you an efficient frontier that’s correct if all of those numbers are correct, but it may be way off if some of those numbers are off (and it’s very sensitive to those numbers).

So, instead of a single number for each return, volatility, and correlation, you try a range of numbers: you have a probability distribution for each return, for each volatility, and for each correlation. Then you run a Monte Carlo simulation: for each iteration you choose a random return for each security (from its probability distribution), a random volatility of returns for each security (from its probability distribution), and a random correlation of returns for each pair of securities (from their probability distributions), and build an efficient frontier for that set of numbers. You do that a bunch of times, getting a bunch of (random) efficient frontiers, then average them together to get your resampled efficient frontier.

The advantages and disadvantages have been cited above.

When I interviewed Harry Markowitz a few years ago he said that:

  • there’s no reason it should work well, but
  • it seems to work pretty well.
#8

great explanation, thank you S2000magician

#9

You’re too kind.

My pleasure.

#10

I have a question here. Is resampled frontier better than regular mean variance frontier? Is it above it or below it?

Thanks,

#11

again better or worse is not a given… there are strengths, and weaknesses.

Strengths: more diversified, more stable (lower transaction costs)

weakness: it lacks ECONOMIC THEORY rationale (there is a statistical rationale…)

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cannot say whether it is above or below … depends on the original mean variance frontier - and how the correction was done.

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Again - most questions do not have a RIGHT answer. There are shades of grey in the answers.

#12

eoc Q 10 ii asks whather resampled frontier is above or below mv ?

#13

I’d say if it is empirically better than it is better regardless of the lack of underlying economic theory (or yet to be discovered).

#14

Assuming you already knew how to build the Efficient Frontier , let me give you a more concrete example:

Let’s say we have 1 billion positions in a portfolio. To build the efficient frontier using all these data points concurrently, it will probably require the computing power from NASA. Now, let’s take 1000 out of this 1 billion positions each time to build an efficient fronier, and we iterate this process maybe 100,000 times (that’s why it’s called resampling because you are doing it over and over again with a random 1000 position from the portfolio. If you think about it, you can actually parallelize this process because the outcome of each set is independent of each other) . At the end, you will have 100,000 set of “Efficient Frontier”. You “average” the position and that gives you the resampled efficient frontier.

#15

Really so the resampling is based on random draws of “mini samples” from the overall population of portfolio stocks? I thought the resampling was based on differing values of mean return, volatility and correlations of the entire portfolio.

So if the mean return, volatility and correlations of the entire portfolio were drawn from a probability ditribution, the efficient frontire was resampled using these random draws and then averaged.

Am I mistaken?

EDIT: Just read S2000magician’s post and that confirms my thoughts.

#16

where did you guys read the monte-carlo bit?

efficient frontier is a single period plot, not multi-period.

my interpretation is you just shift return estimations (e.g. +0.5%, -0.5%, +2% -2% etc) and observe the dispersion of your results.

#17

How else do you think that you do the sampling?

Yes: you do sampling of returns, volatilities, and correlations for a single period, and the sampling is generally done using Monte Carlo simulation.