May 2nd, 2009, 6:53 am
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)
Last edited by
gs2440 on May 1st, 2009, 10:00 pm, edited 1 time in total.