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Either or both assets have are "risk-free" (in the sense of zero volatility, or guaranteed short-term returns). One could then build a portfolio using it/these, ignoring risky assets. If the assets are perfectly correlated, or perfectly negatively correlated, AND you have confidence in their volatilities, then one could construct a zero vol ...

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Risk-free assets refer to assets with a definite rate of return and no risk of default. 　　From the perspective of mathematical statistics, risk-free assets refer to assets with zero variance or standard deviation of investment returns. Of course, the covariance and correlation coefficient between the rate of return of risk-free assets and the rate of return ...

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There are two kinds of factors. Named or defined factors are related to observable economic or financial variables, such as FamaFrench HMB, or the market factor or an oil price factor. Unnamed or statistically identified factors are the result of a PCA using only stock prices. Although the first PCA factor is usually close the Market factor mentioned above (...

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If I understand correctly your question is: Question If I ran PCA and someone else runs PCA and the result is completely different then what good is PCA? Does it make sense to use it for risk management? Answer If you would get a different outcome due to small changes in the data it would be bad measure. However, what people (hopefully) found that use PCA in ...

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EDITED Let $x$ be the available investor's wealth. Given a benchmark $B$ which can be considered as a proxy to the market portfolio, let $x_B$ the amount of invested wealth. Let also $\mu_b$ and $\sigma^2_B$ be the expected return and variance of $B$, respectively. The investor solves a trade off between investing and not investing by considering the risk-...

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I understand that you want to derive some form of risk preference parameter from portfolios that you can observe 'in the wild', and I will discuss that accordingly. As a side note, there is a whole thread in the literature that discusses elicitability of risk preferences using cleverly designed choice experiments -- and the form of the utility function. The ...

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