Measurement Issues In The Capital Asset Pricing Model & Size Effect And Duration
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It has been observed that the value of an asset's beta varies with the frequency of the data used to generate the value, a phenomenon hereafter referred to as "time scale", or simply "scale". If the scale effect is strong enough, then ignoring this phenomenon calls into question studies that rely on comparing beta values. The most notable of these studies is the classification of stocks as "aggressive" or "defensive". I show that such a categorization varies substantially when comparing betas estimated using monthly data versus annual data. Contrary to other studies, betas do not vary monotonically as data scale lengthens. Betas measured on a trailing forty eight month return series with a quarterly time scale explained expected stock returns better than other month data lengths and frequencies. Between 1926 and 2009, beta was able to explain expected returns in 79.1% of rolling estimation periods.Firm size is another important scaling factor that can impact beta measurement. I therefore study stock growth rates based on the size of the underlying firm. I show that cumulative growth factors extracted from firm size are related to Macaulay duration. Smaller firms have a higher duration, and this is shown to explain the small firm effect. Duration relates to reinvestment risk. Using a firm's duration, investors are able to generate home-made dividends when they rebalance their portfolios.