Can someone explain me the mechanics behind getting the resampled efficient frontier? The CFAI text discussion is too obtuse and Schweser seems like outright drivel. All I understand is that we start from historical values of return, variances and correlations and assume that they represent the population mean. Then we make a statistically untenable assumption that expected values of these parameters are same as historical values. In any case, this is then used to get the efficient frontier. Then we do something that I don’t understand. Then we have lots of efficient portfolios corresponding to one given value of expected return. We then average the asset class weights across these portfolios. And we have something better than unconstrained MVO. What and why, I don’t know. Thanks for filling in the blanks!
This is how i see it. Each asset has a distribution of returns. What MVO probably does (atleast that is how i understand it) Ran 100 simulations. Each simulation 1) Pick return for each asset from corresponding return distribution, take historical risk (not sure about this one) and build efficient frontier with this information After 100 iteration you have 100 efficient frontiers. Now you can group points with similar risk and then average returns amount this points. This will give you a resampled efficient frontier Again, this is just my understanding and might be completely off target
Thanks, I was thinking along the same lines. I think I get it - it is combination Monte Carlo (kinda) and MVO. (1) Start with the distribution of historical returns for each asset class along with historical estimates of variances and correlations. (2) Draw a value for return of an asset class from the return distribution for that asset class. Assume this value is the expected return on that asset class. (3) Run MVO to obtain an efficient frontier. Calculate asset allocations for some specific number of efficient portfolios. Say 10. Rank these by return-risk characteristics. (4) Go back to (1) and repeat 100 times. (5) You now have 100 sets of 10 efficient portfolios. Each set is has its constituents portfolios ranked by return-risk characteristics. (6) Take the 10 portfolios that are ranked 1. Presumably they have similar return-risk characteristics. Average asset weights across these 10 portfolios to obtain a resampled efficient portfolio. (7) Repeat (6) for portfolios ranked 2 and so on. (8) At this point you have 10 resampled efficient portfolios, which give us the resampled efficient frontier. Advantages: More stable with respect to time. More stable with respect to inputs. Higher degree of diversification as all asset classes are likely to be represented. Disadvantages: No theoretical basis, esp. for using historical returns as expected returns. Complex.
Questions below. CFAAtlanta Wrote: ------------------------------------------------------- > Thanks, I was thinking along the same lines. I > think I get it - it is combination Monte Carlo > (kinda) and MVO. > > (1) Start with the distribution of historical > returns for each asset class along with historical > estimates of variances and correlations. > (2) Draw a value for return of an asset class from > the return distribution for that asset class. > Assume this value is the expected return on that > asset class. I thought we get the mean return of each asset class rather than getting a sample? eg. if we have returns over 10 years, we get the average return as the input to (3) below? > (3) Run MVO to obtain an efficient frontier. > Calculate asset allocations for some specific > number of efficient portfolios. Say 10. Rank these > by return-risk characteristics. - sticky
Sticky, Let’s say you are right. Then how would you do multiple simulations? Once you have used your one mean return, you are done. You will have one efficient portfolio and nothing to average?
CFAAtlanta Wrote: ------------------------------------------------------- > Sticky, > > Let’s say you are right. Then how would you do > multiple simulations? Once you have used your one > mean return, you are done. You will have one > efficient portfolio and nothing to average? You’ve got a very good question. Actually I don’t understand this myself 
… This is what I **thought** is happening ----- Before you perform a single MVO, you need to obtain a good estimate for the following: 1. each asset’s return 2. each asset’s sd 3. all the correlations between any 2 assets Now if you have 10 years’ annual historical returns (ie 10 data) for each asset, how do you get these inputs for your MVO? For (2), you can ONLY use the 10 returns of asset A to come up to SD of asset A. And repeat for other assets. For (3), you can ONLY use the the 10 returns of A and 10 returns of B and find out their correlation, through, say, regression. And repeat this until you have picked all possible pairs of assets. So you have been using ALL historical data in getting estimates for (2) and (3). As for (1), question is: why are you NOT using all 10 data to get the (average) return of asset A, but just get one of the 10 data as your estimate to (1) for asset A? This is the point I can’t go further. Sampling one return out of the 10 as the return estimate for asset A seems even more inaccurate than taking the average. So it seems like a single MVO using average returns is “the best we can do based on historical data”. The resampled EF method sounds more “stable” as it performs average, but if you are just using “less accurate” returns as input to REF, what’s the point? As you can tell, doing average means you can’t do resampling, but doing resampling by sampling a return from historical data sounds meaningless. I really hope sb could shed light on this. - sticky
as the sayin goes… “Two heads r better than one”, so more samples are better than one i) Resampled efficient portfolio construction is not a complex methodology, so no question of using distributions and monte carlo (this might be a forerunner to monte carlo). ii) We have two constraints viz, the Return and the Risk. We want to maximize the return for a given level of risk. Let us consider ‘x%’ as the required return and ‘y’ as the max risk (SD). Let us consider that we have 3 assets / portfolios with r1%,r2% & r3% of historical returns, let d1,d2 & d3 be the respective SD. Let us consider we take 4 samples from the three assets / portfolios such that (w11*x1)+(w12*x2)+(w13*x3)=x% (w21*x1)+(w22*x2)+(w23*x3)=x% (w31*x1)+(w32*x2)+(w33*x3)=x% (w41*x1)+(w42*x2)+(w43*x3)=x% and (w11*d1)+(w12*d2)+(w13*d3)=y (w21*d1)+(w22*d2)+(w23*d3)=y (w31*d1)+(w32*d2)+(w33*d3)=y (w41*d1)+(w42*d2)+(w43*d3)=y What the resampled effecient portfolio construction says that the final portfolio will have (w11+w21+w31+w41)/4 weight of asset / portfolio 1 (w12+w22+w32+w42)/4 weight of asset / portfolio 2 (w13+w23+w33+w43)/4 weight of asset / portfolio 3 schweser also says that there is no statistical basis for the averaging, i.e. averaging over several samples will not be able to give u better results i.e. Your portfolio will still be on the efficient frontier and not above it… but i guess the averaging must affect the correlation between the assets in the final portfolio i.e. the correlation formula assumes that both the assets will have the same weights… so, with different weights for the assets, we might actually end with low final correlation among the assets…
thanks for the reply. Question below … manjunath.gaddi Wrote: ------------------------------------------------------- > Let us consider ‘x%’ as the required return and > ‘y’ as the max risk (SD). I suppose this is a typo? ‘y’ should be the minimum risk? > Let us consider that we > have 3 assets / portfolios with r1%,r2% & r3% of > historical returns, This is the question I don’t understand here ---- how do you get these r1, r2, r3 for the assets? > let d1,d2 & d3 be the > respective SD. as a side question, how do you get these d1, d2 and d3? > Let us consider we take 4 samples from the three > assets / portfolios such that > > (w11*x1)+(w12*x2)+(w13*x3)=x% > (w21*x1)+(w22*x2)+(w23*x3)=x% > (w31*x1)+(w32*x2)+(w33*x3)=x% > (w41*x1)+(w42*x2)+(w43*x3)=x% > > and > > (w11*d1)+(w12*d2)+(w13*d3)=y > (w21*d1)+(w22*d2)+(w23*d3)=y > (w31*d1)+(w32*d2)+(w33*d3)=y > (w41*d1)+(w42*d2)+(w43*d3)=y I thought under MVO, there is an “optimzier” that can directly calculate w1, w2, w3 to arrive at minimum sd for a required return x%? Why do we need to “sample” so many times? > What the resampled effecient portfolio > construction says that > > the final portfolio will have > (w11+w21+w31+w41)/4 weight of asset / portfolio 1 > (w12+w22+w32+w42)/4 weight of asset / portfolio 2 > (w13+w23+w33+w43)/4 weight of asset / portfolio 3 I understand these follow-up procedures. I just don’t understand the how and why in the initial steps. - sticky
manju, (1) your equations for standard deviations are incorrect as the correlations are missing. Or is this by design, in your opinion? (2) the four portfolios you create by assigning weights to three asset classes - are these weights pulled out of the air? Where is the MVO? (3) How can averaging weights of an asset class effect its correlation with others? Doesn’t make sense. Is this based on your understanding of what’s given in Schweser or is it some other source? Because what you say doesn’t agree with CFAI text (I think).
So is this the Michaud stuff they are asking about? I suppose that this is the downside to patenting some algorithm. Hard to believe they would test you on it since it would then involve paying that prick.
CFAAtlanta Wrote: ------------------------------------------------------- > manju, > > (3) How can averaging weights of an asset class > effect its correlation with others? Doesn’t make > sense. I think when manju said "the averaging must affect the correlation between the assets in the final portfolio " he actually meant “the averaging must affect the SD of the final portfolio”. The fact is that after the averaging of the weightings (under return zone r%), we should be able to locate THAT point along “final” REF with return = r%. manju? > Is this based on your understanding of what’s > given in Schweser or is it some other source? > Because what you say doesn’t agree with CFAI text > (I think). Or other reference? - sticky
It is the Milchaud stuff. I think Joey is right - they cannot test this topic other than perhaps asking us to list advantages/disadvantages.
I hate this stuff. I bought that book and then spent the whole time stewing about how someone thinks they can patent something like that. We’ve got people like Efron and Markowitz out there without any patents (as far as I know) and this guy thinks he can patent something that is an out growth of all those other people’s unpatented work?
I read Schweser (p.152, book 2) for my 20th time just now. Found bits that make perfect sense but others don’t to me. Let me list them here. I am getting personal about this REF … >.< 1. “… the manager uses historical returns, sd, and p, assuming they are true historical values.” comment: this seems fine 2. “The manager specifies returns on the EF and then, using historical data, has the computer generate a set of mean variance efficient portfolio; each portfolio (combination of assets) has the minimum standard deviation for the given stated return.” Comment: my confusion starts here. Is the computer given averaged the averaged return for each asset, or just a sampled return (as mentioned by CFAAtlanta) for each asset? The minimum SD for each of the specified returns have been found by computer (the optimizer), so is this not the end of the story? It seems this is the best EF we can achieve. Why go on? 3. "As you can imagine, there can be many different combination (by varying the weights) of a given set of asssets that will yield the same expected return and sd, so the computer is asked for another set of mean-variance efficient portfolio (a resampled EF) using the same set of returns and sd. Comment: I really can’t “imagine” this. If the sd from computer has been the minimal sd for a given stated return r%, are there really numerous other asset combinations to achieve the same [r, sd]? Note that we are giving the SAME set of returns, SDs to the computer. 4. “Each run generates another EF and each asset has a different weight in each EF” Comment: Well I “literally” agree, provided that I try to follow the logic before 5. “The manager notes the weights of asset 1 in a ll the EFs and average them.” Comment: “literally” agree 6. “He proceeds to the next asset and finds its average weight and so on until he has an average weight for each individual asset in the set of EFs” Comment: “literally” agree. Anyone of help? Found Joey and CFAAtlanta’s other posts and I agree this won’t show up in the exam — other than asking for advantage/disadvantages. - sticky
sorry I didnt write this major assumption earlier: The asset / portfolio already lies on the efficient frontier with the same risk - return requirements. i.e. r1=r2=r3=x and d1=d2=d3=y regarding point 1) Pls refer to SD calculation in Page 157 and the professor note in page 158, Book 2 , Schweser… (SD calculation by this method would refer to max SD) regarding point 2) these weights are not pulled out of air but actually needs to be solved for… let me illustrate this with an example: Initially, there are no portfolios, I need to create a portfolio which is on the efficient frontier using US Equities, US Bonds, Intl Equities and Intl Bonds as 4 asset classes. So, I’m able to create 3 portfolios with different weights of US Equities, US Bonds, Intl Equities and Intl Bonds say and all three of them on the efficient frontier. From this point onwards the re sampling happens: I’m using 4 samples (w11*r1)+(w12*r2)+(w13*r3)=x% (w21*r1)+(w22*r2)+(w23*r3)=x% (w31*r1)+(w32*r2)+(w33*r3)=x% (w41*r1)+(w42*r2)+(w43*r3)=x% and (w11*d1)+(w12*d2)+(w13*d3)=y (w21*d1)+(w22*d2)+(w23*d3)=y (w31*d1)+(w32*d2)+(w33*d3)=y (w41*d1)+(w42*d2)+(w43*d3)=y coming to sticky’s why: If we use one of the portfolios created before re sampling, there is a possibility that one of the asset class’s weight might be zero, but by resampling the possibility of any asset class of being zero in the final portfolio is considerably less. So, with a resampled efficient portfolio the possibility of having assets from all the asset classes is more. (more diversification but not as much as you would get in black litterman) regarding point 3) I stand corrected. Averaging and correlation has a correlation of 0.
manjunath.gaddi Wrote: ------------------------------------------------------- > sorry I didnt write this major assumption > earlier: > > The asset / portfolio already lies on the > efficient frontier with the same risk - return > requirements. > > i.e. r1=r2=r3=x and d1=d2=d3=y That makes sense under “resampled efficient frontier” — you have the multiple REFs ready (after something that I don’t understand) and you get the asset weights from each of the REF points with r% return. This part I understand. As you can tell from my previous posts, I don’t understand the how and why of getting these multiple REFs. > regarding point 1) Pls refer to SD calculation in > Page 157 and the professor note in page 158, Book > 2 , Schweser… (SD calculation by this method > would refer to max SD) I think this gets mixed up. (a) You and Schweser p.158 are talking about getting the SD of a portfolio BETWEEN 2 corner portfolios, based on known weightings of the 2 corner portfolios. In doing this, the EF is already ready, the corner portfolios are already ready. On the other hand, CFAAtlanta’s question (1) is about getting SDs of mixture of “raw assets” ---- so that the EF (resampled or not) can be worked out. In getting the SDs at this stage, “the manager uses historical returns, sds, and CORRELEATIONS …” (2nd paragraph, p.152, book 2) (b) though not related to REF, this “max sd” mentioned on Schweser p.158 is just a compromise on the SD, simply because of the simpler, straight line approach that we are using between 2 corner portfolios. Because we do not put in correlation in calculating the SD, there is not diversification benefit here and so the resulting SD is max. Again, NOTHING to do with getting a MINIMUM SD when we are to plot an EF or REF. > regarding point 2) these weights are not pulled > out of air but actually needs to be solved > for… This is my question What inputs are you having EACH TIME you solve it? > let me illustrate this with an example: > Initially, there are no portfolios, I need to > create a portfolio which is on the efficient > frontier using US Equities, US Bonds, Intl > Equities and Intl Bonds as 4 asset classes. > > So, I’m able to create 3 portfolios with different > weights of US Equities, US Bonds, Intl Equities > and Intl Bonds say and all three of them on the > efficient frontier. > > From this point onwards the re sampling happens: > I’m using 4 samples > > (w11*r1)+(w12*r2)+(w13*r3)=x% > (w21*r1)+(w22*r2)+(w23*r3)=x% > (w31*r1)+(w32*r2)+(w33*r3)=x% > (w41*r1)+(w42*r2)+(w43*r3)=x% > > and > > (w11*d1)+(w12*d2)+(w13*d3)=y > (w21*d1)+(w22*d2)+(w23*d3)=y > (w31*d1)+(w32*d2)+(w33*d3)=y > (w41*d1)+(w42*d2)+(w43*d3)=y > > > coming to sticky’s why: > > If we use one of the portfolios created before re > sampling, there is a possibility that one of the > asset class’s weight might be zero, but by > resampling the possibility of any asset class of > being zero in the final portfolio is considerably > less. If that portfolio (with zero weighting for some assets) is on an EF, that means provided the required return x%, this sd=y will be the smallest I can get. I am done. Why bother including that useless asset? > So, with a resampled efficient portfolio the > possibility of having assets from all the asset > classes is more. (more diversification but not as > much as you would get in black litterman) I have similar question for this but let’s get the previous ones sorted out first. > regarding point 3) I stand corrected. Averaging > and correlation has a correlation of 0. Don’t understand what you are saying here. - sticky
Guys, just dont sweat over this too much. all that you will be asked(if at all) would be to explain how it works. Let us say you have computed the frontier using a set of inputs E®, Sd, corr, and that you have portfolios on the frontier with certain asset class combinations. You may have used the return and other estimates using some historical data. This is just a good guess. so to get somekind of average, you vary these returns and recompute the efficient frontier. How you vary the input is up to you. probably if you looked at the 20 year hist avg to start with, you can break it up to 5 yr sub period. you may see a trend. based on the trend and other available informations, you can estimate the inputs to go one way or the other and by certain amount… all that we may have to say is that the resampled efficient frontier is constructed by varying the input around the original estimate and then taking the mean of the weights for the different asset clasesses for each portfolio… I hope I have not confused you further…
i agree w/ krishna…CFA is testing you on CFA materials…you’re not expected to research the concept from scratch