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When taking capital budgeting decisions appropriate cost of capital should depend on the horizon of the investment. So the beta of a stock, i.e. it's covariance with the market should depend on the horizon of the investment.

For some stocks, beta might be declining with maturity. For others, beta might be increasing with maturity. Is there any literature out there that talks about this issues? Why economically and fundamentally, beta for a company at different horizons might differ?

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If your issue is the holding period "sensibility", I don't have persuasive economic/fundamental motivation about it. It's an interesting question. Anyway in econometric point of view the issue is part of instability parameters problem. If the time horizon for your investment project is, for example, one year, then you need return and beta one year based. Therefore, in simplest way, you have to take yearly data return to estimate the beta, with certain historical depth. However the beta are not (explicitly) time horizon dependent and you can take the monthly/weekly/daily data. In my experience the time frequency are not so important in beta estimate (also if the number of observation change and this tend to suggest, at least in my opinion, weekly or daily data ... but monthly are largely used). In opposite is so important the historical depth. This problem is strictly related with time varying variance and correlation. However the "beta structure" and experience suggest that it move around one and this fact alleviate the problem. You can see for example Blume's technique. Maybe if your time horizon is too long the better choice for beta becomes 1.

In any case, for example and at least in the past, Merrill Lynch suggest to use monthly data with 60 obs. In the past I looked for but I'm not found empirical research for support them choice.

Hope that helps

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Hmm, I guess you're trying to determine the cost of capital using CAPM. Generally speaking, beta should stabilize for mature companies. Personally, I like to use an adjusted beta, eg: 1/3*current_beta + 2/3 to reflect this.

Beta of a stock is just a measure of how it's covariance is affected compared to the market's volatility as you pointed out. Here's a link from Investopedia about calculating beta: http://www.investopedia.com/ask/answers/070615/what-formula-calculating-beta.asp

Since it is clearly a function of market dynamics, beta is often subject to the whims of investors, and sometimes rightfully. Mature companies can go either way -- imagine a major lawsuit that affects a well established public company. A high profile case could cause the volatility of the stock to be extremely volatile for many months in a "serene" market causing its beta to jump.

Hope that helps.

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  • $\begingroup$ This is not what I am looking for. The shrinking is fine for most corporate finance applications. I am looking to the question through the lens of an academic. Why fundamentally stocks have different systematic risks at different horizons? $\endgroup$ – phdstudent Mar 12 '16 at 14:23
  • $\begingroup$ Pardon me if you already know this. In the risk layering concept, Systematic risk is something that cannot be eliminated and therefore applies to the broader market. Any company has additional types of risk - operational risk, currency risk, etc thus beta > 1. If you got rid off all of that as the company matures, you would be left only with systematic risk, i.e. Beta=1. Uniformity with the markets comes with growth and maturity of companies. $\endgroup$ – clocker Mar 12 '16 at 19:01
  • $\begingroup$ @Mahnud, that's not true the beta can be lower than 1 and theoretically speaking it can be even negative. An example of veta lower than 1 is gold. In the other hand one way of measuring the change of the beta during time is using dinamic linear models like kalaman filter. For "forecast" purposes depending with the maturity I'm not sure how to do it, you can forecast with Kalaman filtering but I don't think that's what you want $\endgroup$ – Alejandro Andrade Mar 24 '16 at 17:26
  • $\begingroup$ You are correct, beta can be less than 1. However, I am referring specifically to stock prices of public companies. Beta is normally measured using the aggregate volatility of 500 companies. If you were to take say the Wiltshire 5000 as the market you would be hard pressed to find a beta < 1. But it is possible; however, long term the company is a market participant and theoretically it's beta should converge to 1. How long it takes is another question. $\endgroup$ – clocker Mar 25 '16 at 19:23

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