# Factor3

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bio website location United States age 35 member for 1 year, 9 months seen Nov 20 at 12:24 profile views 11

 Nov19 comment Why do stocks with a negative beta return less than the risk free rate? They don't have the same "risk"... risk (from a perspective of $\beta$) is having a low payoff when consumption is low, and a high payoff when consumption is "high." Nov19 comment Why do stocks with a negative beta return less than the risk free rate? Stock B does have the same risk of bad returns... but they occur in states of converse consumption levels. Think of an insurance policy, I pay 10 per mo and if I die my spouse gets 100,000. In the event I die, my wife will have made the return of $\frac{100,000}{10 x num premiums I paid} - 1$. Otherwise, her rate of return is a loss of every penny we've invested in the policy. You refer to a $\beta$ "to the market" which has a very specific meaning: "correlated to the aggregate market, i.e. systematic risk." Remember, Stock B only pays you less in the event the market appreciates. May7 comment Rate Distortion Minimization in a Python Clustering Algorithm May7 comment Rate Distortion Minimization in a Python Clustering Algorithm When you say my "observations aren't independent now", I'm not sure what you're referring to. I'm running a clustering algorithm on a correlation matrix, which I would call my "observations," and asset returns in finance are rarely (if ever) independent, so I'm not quite sure what you mean. May7 comment Rate Distortion Minimization in a Python Clustering Algorithm @quasi, thanks for the reply. A little clarification, $\mathbf{\Sigma}$ as I've defined it, is the covariance matrix as an input to the distortion calculation. The clustering algorithm is being run on the correlation matrix of asset returns. So you're saying, I should set $\mathbf{\Sigma}$ equal to the Covariance of the correlation matrix (which is the input to my clustering algorithm), instead of the covariance of asset returns (which I'm currently doing), correct? May7 comment Rate Distortion Minimization in a Python Clustering Algorithm Just posted the data, as well as a small script to show you exactly what I'm seeing (as well as the output). Thanks for the suggestion @quasi Feb16 comment Computing the Sharpe Ratio step 1: Calculate log returns step 2: calculate volatility on log returns step 3: apply time scaling to volatility (i.e. $\sigma\cdot\sqrt{52}$) step 4: convert log returns to appropriate time scaled estimate (i.e. $r_{\textrm{daily}}\cdot252 = r_{\textrm{annual}}$ to the same time scale as volatility in step 3) step 5: convert log to geometric returns via $r_{\textrm{geometric}}=e^{r_{\textrm{log returns}}}-1$ for use in ex-post Sharpe Ratio Feb16 comment Computing the Sharpe Ratio @Freddy, thanks for the positive feedback. Personally, I think it's really a question of accuracy and estimation consistency. If I want to accurately estimate a r.v. (Sharpe Ratio in this case), I might also want to simulate future realizations using simulation techniques, in which case getting the distribution and respective moments correct seems pretty important to me. Why is $\frac{P_t}{P_{t-1}}-1$, easier to calculate than $\log(\frac{P_t}{P_{t-1}})$?It's all calculated from the price series, and neither is more computationally costly, even if using an excel spreadsheet.