With respect to CFA chapter 26, question 10, why can’t biases result in a higher frontier than that generated through perfect infromation? That is, why can’t the inputs for MV analysis yield more optimistic expectations than would be yielded through perfect info?
I think it’s because the actual frontier exists regardless of the models or inputs we use. You can’t get above it. Inferior models can only make your worse off.
Because the frontier calculated with MV contain estimation errors (expected return for example), so it must lie below (less efficient) than a frontier reflecting the true parameters (perfect info)
I am also confused with this. why people can not underestimate the standard deviation, or overestimate the return?
I am also confused with this. why people can not underestimate the standard deviation, or overestimate the return?
rivercharlesy Wrote: ------------------------------------------------------- > I am also confused with this. why people can not > underestimate the standard deviation, or > overestimate the return? The idea is simple. If you have perfect knowlege, you can build best portfolios. For example, you have two assets that are perfectly correlated A and B. They have same volatility that you correctly estimate at 10% and true returns muA = 10% and muB = 8%. The best you can do is to invest 100% in muA and get 10% return with 10% volatility. That would be the point on the actual efficient frontier. Now let’s assume you accurately estimate return of A estmuA = 10% but incorrectly overestimate the return of B estmuB = 3000%. You would put all your money in B expecting huge returns but in fact you would only make 8% because that’s the true return of B. Does that help?
Thanks, I had confusion before, but now I have a better understanding. For this Q, I think there two kinds of “Efficient Frontiers”: 1) The Efficient Frontier is based on the unbiased and perfect knowledge. That’s the EF we learnt from L1. 2) Other “Efficient Frontiers” is based on the biased or false information. These “Efficient Frontiers” have to be adjusted, so all are “compatible”. So, the EF in 1) is above all others. Without some adjustment, I can plot the EF anywhere according to my version(biased) of expectation. PS. 1) elcfa’s explanation is better than CFAI’s answer (10.A.ii) on P341. 2) BTW, the results of MVO are most sensitive to E(Ri) inputs; but Sharpe Ratio is usually gamed with SD. In my words, it’s easy to make from E(Ri) and SD; but it's not worth to make from E(SD) and Ri. :DD
but since efficient frontier is based on perfect knowledge - anything that is based off of imperfect information should no longer be considered EFFICIENT. So please stop calling them a “personal efficient frontier” if you will. (or like you have). There is only one efficient frontier, and since the amount of information needed (# of returns, # of variances, # of covariances) is large - there is an issue. additionally - the efficient frontier itself is very sensitive to the input parameters… those lead to the issue that any frontier based on sampled returns, is likely to lie below the efficient frontier).
Just for fun:D Mean-Variance Efficient Frontier in Matlab 1) Construct Hypothetical 3-Asset Universe 2) Calculate Efficient Frontier 3) Randomize Asset Weights 4) Compute Expected Portfolio Returns / Risks 5) Compare Risk-Return Results with Efficient Frontier —start of matlab code— returns = [0.1 0.15 0.12]; STDs = [0.2 0.25 0.18]; correlations = [1 0.3 0.4 0.3 1 0.3 0.4 0.3 1]; % Convert to variance-covariance matrix % Convert the standard deviations and correlation covariances = corr2cov(STDs , correlations); portopt(returns , covariances , 20) weights = exprnd(1,1000,3); total = sum(weights , 2); total = total(:,ones(3,1)); weights = weights./total; [portRisk , portReturn] = portstats(returns , covariances , weights); hold on plot(portRisk , portReturn , ‘.r’) title(‘Mean-Variance Efficient Frontier and Random Portfolios’) hold off —end of matlab code— http://www.mathworks.com/products/finance/demos.html?file=/products/demos/shipping/finance/ftgex1.html#3 PS. Matlab is not my favorite tool, but this code works in my matlab IDE. I’ll try it for the Sharpe Ratio gaming after June 4.