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The asset rate of returns is the profit on a particular investment; it includes any change in the asset value, interest, commission or dividends and so, all other cash-flows which an investors receive or pays due to the investment.

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There are three reasons to use the logarithmic transformation of returns. First, custom says to use it. … There is nothing wrong with using log-returns; in fact, it is a good decision in some models because of how they are built. …
answered Feb 14 '21 by Dave Harris
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You can use Bayesian methods. Missing data is not an intrinsic problem for Bayesian methods, however, you do need to understand why the data is missing before you use Bayesian methods. In your case, …
answered Nov 12 '17 by Dave Harris
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So, let me begin by stating that the distribution for returns has been derived and solved. … The distribution of returns, or price returns plus dividend returns as in IRR, in equilibrium, ignoring bankruptcy, merger and liquidity risks, is $$\left[\frac{\pi}{2}+\tan^{-1}\left(\frac{\mu}{\sigma …
answered Dec 6 '16 by Dave Harris
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I have written an entire paper on this approach at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2828744 As to your specifics 1) "Volatility" as defined by variance does not exist, which is wh …
answered Jun 18 '17 by Dave Harris
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If you are missing a price for one security on July 27, and you are calculating returns as $\frac{p_{27}}{p_{26}}-1$ and $\frac{p_{28}}{p_{27}}-1$ you have two choices. … You could change the likelihood function and solve $$\sqrt{\frac{p_{28}}{p_{26}}}-1,$$ or you could leave both returns blank. …
answered Sep 22 '19 by Dave Harris
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For my article on this, you can find it at: Harris, D.E. (2017) The Distribution of Returns. … As to estimating the scale parameter of returns, you cannot use a non-Bayesian method. There does not exist an unbiased admissible Frequentist estimator for real data. …
answered Jan 21 '18 by Dave Harris
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If returns are r(P1,P2) and (P1,P2) follow a Brownian motion, then it is proven that planar Brownian motion is the only Brownian motion that is not ergodic. …
answered May 7 '21 by Dave Harris
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It is at Harris, D.E.(2017) The Distribution of Returns. Journal of Mathematical Finance , 7, 769-804. … It does depend upon whether you calculate returns as $$r=\frac{p_{t+1}}{p_t},$$ or $$r=\log(p_{t+1})-\log(p_t)$$ or $$p_{t+1}=rp_t+\epsilon_{t+1}.$$ Each one generates a different answer. …
answered Dec 6 '17 by Dave Harris
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}_{t+1}\times\text{Quantity}_{t+1}=p_{t+1}q_{t+1}.$$ So $$R(p_t,p_{t+1},q_t,q_{t+1})=\frac{p_{t+1}q_{t+1}}{p_tq_t}$$ So returns are a function of prices and quantities. … You are correct, the normal distribution cannot be the distribution of returns. You haven't missed anything. …
answered Apr 1 '19 by Dave Harris
3
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If the parameters are unknown, then it is possible to derive the distribution of returns. … As such, returns are not data; they are statistics. Their distribution should be derived. …
answered May 21 '19 by Dave Harris
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I have done that. The distribution if there are no dividends, mergers or bankruptcy and if liquidity costs are ignored is $$\Pr(r|r^*;\gamma)=\left[\frac{\pi}{2}+\tan^{-1}\left(\frac{r^*}{\gamma}\rig …
answered Apr 21 '21 by Dave Harris