I am trying calculate expected return and risk (stdev) based on historical data using Mean Variance Analysis framework. Let's say the portfolio has 10 stocks, 9 of them have more than 10 years history but one of them only have 1 month historical data. If I want every stock has the same length of historical data for correlation matrix, shall i just use 1 month of data to estimate? or fill the one with short historical data with 0?
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1 Answer
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There are two common solutions.
You exclude from your universe stocks whose history is too short (i.e. only recently went public). Sometimes it breaks your heart to do that, because you really like the stock. (If the time series is long enough, but still has small gaps, there are ways to "fix" the covariance matrix.)
You use models to predict the covariance. The most famous example of this approach is MSCI Barra predicted beta (see, for example, https://doi.org/10.3905/jpm.2014.41.1.057 for its description). However they don't try to predict the covarance to all other stocks. Rather, they use multifactor model, and predict, based on fundamentals, the correlation to the few factors that they assume to drive the market. They do it right at IPO time with no history.
answered May 4, 2021 at 5:23
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$\begingroup$ Dimitri, thank you very much for the answer. What is your comments on assume missing value to be zero? $\endgroup$ Commented May 4, 2021 at 5:37
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$\begingroup$ I'm not comfortable with making up data. What do you assume to be 0 - the returns? Or the correlations? The goal is to assume that the future will ave similar characteristics to the historical past, but there's no reason why the future would be like any made-up 0's. $\endgroup$ Commented May 4, 2021 at 5:44
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$\begingroup$ I was naively assuming the returns are 0 since the securities are not there in past. But totally agree with you that it's not adding value in terms of representing future. The limitation of my calculation is that, 1). i don't have the advance tool you mentioned in solution 2; 2) i can give up the security with short time series; 3).if i just use 1 month length time series for all 10 stocks, the return and risk are absurd. Anyways, thanks Dimitri, your help are instrumental. $\endgroup$ Commented May 4, 2021 at 6:03
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$\begingroup$ Great answer, since I haв exactly the same question. Is there some rule of thumb or maybe a paper on how many data points (days, weeks, months) at the minimum you must have to arrive to somewhat sane results? $\endgroup$– ruslanivCommented Jun 14, 2021 at 11:53