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What you observe in your regression is not strange at all. The regression beta you estimated is $\beta_i = \frac {\mathrm{cov}(r_i,r_m)}{\mathrm{var}(r_m)}$ where $i$ represents the country/region (such as the USA or China) and $m$ represents the "market" (which you take to be the ACWI). Since the USA is itself such a large component of the ACWI (about ...
There is a rationale here and it has to do with the connection between diversification and the number of assets in a portfolio. Suppose we purchase an equal-weighted portfolio of n stocks. The variance of the return is then: $\sigma_{p}^2$ = $\sum$ $\sum$ $w_i$$w_jCov(R_i,R_j) In the above notation, the sigmas are summing over i and j ... 3 Beta as a measure of risk has serious drawbacks, particularly in emerging markets. You need to consider alternative risk metrics (cost-of-capital build-up method or volatility, for example), or if you do use beta consider what the market index refers to and the composition of that index. This paper actually happens to touch on beta estimation and uses ... 2 Assuming those are arithmetic returns and covariances at the horizon, calculate a 9\times1 vector containing the betas with respect to the world index using the covariance matrix, call it \beta. The covariance resulting from the world index can be described as \beta\sigma_{world}^{2}\beta'. The matrix ... 1 Your formula is adding where you should be multiplying, and you plugged your inputs into the wrong places (your levered Beta notably). In any case, the process for un-levering/re-levering the beta goes like so: Step 1: Find benchmark company/asset/project Beta. Step 2: Un-lever the benchmark Beta: Unlevered Beta = Levered Beta * (1 / ( 1 + (1 - ... 1 you get what should get. You can't prove that strategy long X short Y is market neutral: is strategy long EUR/USD short USD/CHF risk neutral? I wouldn't say that. It depends, on what? On relationship between these variables, so it is perfectly hedged only if dX=dY so your task is bad stated: it should be rather: what should be b to assure that ... 1 The efficient frontier should be expressed in terms of arithmetic returns since only these returns can account for cross-sectional aggregation. Hence, if you assume the log returns of the risky portfolio are X_{p} \sim N(\mu,\sigma^{2}), then you first have to convert it to log-normal moments before combining it with the risk-free rate, r_{f}. However, ... 1 I'm not sure what you mean exactly by "does it matter...", but generally speaking it should not surprise you that your alpha is not significant, as many trading strategies are more or less "transformations" of beta. In the purest sense, alpha is not easy to accomplish, and various forms of the EMH would say that it is nearly impossible to achieve it for a ... 1 No, the "low-beta" anomaly is not the result of the difference between arithmetic and geometric mean returns. Statistical tests verifying the existence of the anomaly rely on models employing the arithmetic mean returns,$$\mu_a = \mu_g + \frac{\sigma^2}{2}$\$, hence the penalty excess volatility incurs when compounding returns over time does not explain the ...