Hi,Black Litterman Model takes the equilibrium portfolio and tilts it to incorporate investors view. I have two questions about this to our erudite members -:1. For any kind of model we give input parameters generally developed based on historical data. For instance in Black Litterman we feed the return vector and Covariance matrix based on historical data sets that we have. How do i deal in a situation where we have very less data; e.g. lets say i want to invest in an asset class of which i have very less data. How do i ensure in this situation that my return vector and covariance matrix are as accurate as possible. Please remember any sort of min variance optimization is very sensitive to accuracy of return vector. 2. I know we can incorporate investors confidence, other than that can i somehow ensure by any other means about the correctness of the view?Cheers,Gaurav

1) This is hard problem and dealing with short history or missing data can be quite challenging. Suppose a stock has less data than (say) 1 year daily then use another index or stock that closely resembles the first one to proxy. On many occasions, you can backfill some of the missing data by using either EM algorithm. 2) Not sure what your question is here but in BL model you can give both your view and the confidence in that view.

Dear Cryptic 26,Thanks for your response it surely does gives a food for thought. However my problem is if data is scarce for my asset class 'X' then how do i establish a replicating stock. I assume here we are talking for a stock with correlation close to 1 with our asset class 'X'. But with scarce data can we say that estimated correlation will not be biased?Its not the case of some data missing in between the real problem is that length of data set (in MATLAB terms) is quite less. Can we still use EM algorithm?Cheers,Gaurav Sinha

QuoteOriginally posted by: gs2440Dear Cryptic 26,Thanks for your response it surely does gives a food for thought. However my problem is if data is scarce for my asset class 'X' then how do i establish a replicating stock. I assume here we are talking for a stock with correlation close to 1 with our asset class 'X'. But with scarce data can we say that estimated correlation will not be biased?Its not the case of some data missing in between the real problem is that length of data set (in MATLAB terms) is quite less. Can we still use EM algorithm?Cheers,Gaurav SinhaNo, in this case EM won't be effective. You will never find perfect correlation in real world. And even if you find, it need not be the same. What you could do is essentially find the beta of the stock with respect to indexes or other stocks. Sometimes, a given industry might in more than one sub sectors such as (e.g) GE.It falls in different domain. Find the best possible indexes or sectors that explain that particular industry or stock. And obtain the risk of the stock in terms of the other indexes. Assume the covariance structure or betas shall be the same (during the time when you don't have data) and obtain the covariance matrix of the entire portfolio. In other words,1) find the covariance or beta of the stock A with available data.2) find the covariance of the remaining stocks using the longer history.3) fill the holes of the covariance of stock A with rest in the block obtained (2). 4) Try to see if your covariance is postive sem definite. If not correct for the same.Done.The procedure of backfilling your return series with the obtained betas is something you could try but it is better to have the risk structure than have the return series. The latter will introduce some errors but you don't have a choice. Try and look at the volatility of the stock in the period that you filled vs. the period it has history. Compare the same with similar stocks in history or a broad based index. Re-scale the volatility if required. This shall minimize some error. Another approach is to find a probability density function to the given return series. Then use the p.d.f to generate simulated return series. This is equally error prone and you could get lucky sometimes. Proxy is the best way though.

QuoteOriginally posted by: cryptic26QuoteOriginally posted by: gs2440Dear Cryptic 26,Thanks for your response it surely does gives a food for thought. However my problem is if data is scarce for my asset class 'X' then how do i establish a replicating stock. I assume here we are talking for a stock with correlation close to 1 with our asset class 'X'. But with scarce data can we say that estimated correlation will not be biased?Its not the case of some data missing in between the real problem is that length of data set (in MATLAB terms) is quite less. Can we still use EM algorithm?Cheers,Gaurav SinhaNo, in this case EM won't be effective. You will never find perfect correlation in real world. And even if you find, it need not be the same. What you could do is essentially find the beta of the stock with respect to indexes or other stocks. Sometimes, a given industry might in more than one sub sectors such as (e.g) GE.It falls in different domain. Find the best possible indexes or sectors that explain that particular industry or stock. And obtain the risk of the stock in terms of the other indexes. Assume the covariance structure or betas shall be the same (during the time when you don't have data) and obtain the covariance matrix of the entire portfolio. In other words,1) find the covariance or beta of the stock A with available data.2) find the covariance of the remaining stocks using the longer history.3) fill the holes of the covariance of stock A with rest in the block obtained (2). 4) Try to see if your covariance is postive sem definite. If not correct for the same.Done.The procedure of backfilling your return series with the obtained betas is something you could try but it is better to have the risk structure than have the return series. The latter will introduce some errors but you don't have a choice. Try and look at the volatility of the stock in the period that you filled vs. the period it has history. Compare the same with similar stocks in history or a broad based index. Re-scale the volatility if required. This shall minimize some error. Another approach is to find a probability density function to the given return series. Then use the p.d.f to generate simulated return series. This is equally error prone and you could get lucky sometimes. Proxy is the best way though.As i get from your reply there are two ways a) Evaluate with whatever data I have the covariance of stock 'X' (stock with little data) and hope that the covariance would be same even for period where 'X' doesn't have a history while other stocks have. So I am all set with a covariance matrix. For returns Evaluate Beta of 'X' with respect to some close index and then back fill for returns using this beta and history of index to get a new complete return series.--> Please correct me if i am wrong hereb) Assume a PDF (or equivalently distribution) for returns; estimate parameters (lets say using MLE) and then generate missing data using distribution and its parameters.This one seems a bit dodgy to me; as essentially you have already assumed the distribution and evaluated distribution parameter's (i.e. mean and sigma for Normal) so whats the need of back filing via simulation, since we already know the 'mean' of the returns. The Co variance can be evaluated with whatever data I have (since we earlier assumed that covariance structure would be same even for previous period)

QuoteOriginally posted by: gs2440 As i get from your reply there are two ways a) Evaluate with whatever data I have the covariance of stock 'X' (stock with little data) and hope that the covariance would be same even for period where 'X' doesn't have a history while other stocks have. So I am all set with a covariance matrix. For returns Evaluate Beta of 'X' with respect to some close index and then back fill for returns using this beta and history of index to get a new complete return series.--> Please correct me if i am wrong here You are right. Quote This one seems a bit dodgy to me; as essentially you have already assumed the distribution and evaluated distribution parameter's (i.e. mean and sigma for Normal) so whats the need of back filing via simulation, since we already know the 'mean' of the returns. The Co variance can be evaluated with whatever data I have (since we earlier assumed that covariance structure would be same even for previous period)You are assuming that normal is the default distribution. The distribution need not be guassian. You might even need to have a mixture of normals, if the data is skewed.

QuoteOriginally posted by: cryptic26QuoteOriginally posted by: gs2440 As i get from your reply there are two ways a) Evaluate with whatever data I have the covariance of stock 'X' (stock with little data) and hope that the covariance would be same even for period where 'X' doesn't have a history while other stocks have. So I am all set with a covariance matrix. For returns Evaluate Beta of 'X' with respect to some close index and then back fill for returns using this beta and history of index to get a new complete return series.--> Please correct me if i am wrong here You are right. Thanks cryptic, that sounds good however i am little skeptic about the rightness of return back filling for 'X' using its Beta with certain index. I tried testing this approach for GE by regressing its return from 1980 to 1995 with S&P and then predicting it from 1995 to 2009 based on the regression estimates from the 1st half. The results obtained were not encouraging and at times the actual return differed from the predicted one by 500% or more.Any thoughts about regression that should be done, i think simple linear regression would not be good enough, would a curve fitting regression suffice closely?

QuoteOriginally posted by: gs2440 Thanks cryptic, that sounds good however i am little skeptic about the rightness of return back filling for 'X' using its Beta with certain index. I tried testing this approach for GE by regressing its return from 1980 to 1995 with S&P and then predicting it from 1995 to 2009 based on the regression estimates from the 1st half. The results obtained were not encouraging and at times the actual return differed from the predicted one by 500% or more.Any thoughts about regression that should be done, i think simple linear regression would not be good enough, would a curve fitting regression suffice closely?Does not surprise me at all. It is very hard to replicate the time series but relatively easy to replicate the covariance structure. Can you also tell me how different the beta of GE was in the two time periods. Also, measure the beta of another security like GE. This is also harder because GE belongs to various sectors. Let's choose SI (siemens) to proxy for GE. Assume you don't have GE in 95-99 and use Siemens beta instead to replicate the risk of GE. The compare it with the actual GE beta from 95-99. Also measure the betas for each year using daily return for both firms. Plot them, see if they compare.

QuoteDoes not surprise me at all. It is very hard to replicate the time series but relatively easy to replicate the covariance structure. Can you also tell me how different the beta of GE was in the two time periods. Also, measure the beta of another security like GE. This is also harder because GE belongs to various sectors. Let's choose SI (siemens) to proxy for GE. Assume you don't have GE in 95-99 and use Siemens beta instead to replicate the risk of GE. The compare it with the actual GE beta from 95-99. Also measure the betas for each year using daily return for both firms. Plot them, see if they compare.The regression coefficients are actually quite close for both blocks 2nd Half 1.09798 -0.00005 and for 1st Half 1.18054 -0.00010 (Beta and alpha respectively). Even then i am getting deviations more than 1000% for predicted values and actual values. I doubt this because of non stationarity of series for GE that we have. Even if we assume series to be Stationary there are bound to be many instances where GE alone was hit and not Index, in these cases our regression estimate is bound to fail.And for Siemens do you mean that instead of GE, Siemen should be regressed against S&P and then used to back fill of data (using this regression coefficient and S&P) for GE and then comparison should be made between the predicted returns (using Siemens beta) vs actual GE returns? That's doesn't makes much sense to me, please explain a bit more.

QuoteOriginally posted by: gs2440 The regression coefficients are actually quite close for both blocks 2nd Half 1.09798 -0.00005 and for 1st Half 1.18054 -0.00010 (Beta and alpha respectively). Even then i am getting deviations more than 1000% for predicted values and actual values. I doubt this because of non stationarity of series for GE that we have. Even if we assume series to be Stationary there are bound to be many instances where GE alone was hit and not Index, in these cases our regression estimate is bound to fail.And for Siemens do you mean that instead of GE, Siemen should be regressed against S&P and then used to back fill of data (using this regression coefficient and S&P) for GE and then comparison should be made between the predicted returns (using Siemens beta) vs actual GE returns? That's doesn't makes much sense to me, please explain a bit more.As I said GE is a hard one. If your betas are close then your specific risk part shall be different in the two periods. Try and replicate the risk (a.k.a use Betas to get your covariance matrix). Also, try to use the small cap and value premium in addition to S&P. I gave the example of Siemens to help you see how close you can get to actual risk by proxy. In this case you have the data of GE and so you can compare the actual vs. hypothetical risk (as measured by Siemens). In your actual problem you don't have this luxury.