Portfolio Management -- short selling necessary, positive, selling, address, problem

liquidity

Schweser Book 5 Page 181: “To address the minimum-variance frontier instability problem, the analyst might consider constraining the portfolio weights (e.g. prohibiting short sales so that all portfolio weights are positive).”
Schweser Book 5 Page 212: Two key assumptions necessary to derive the CAPM are 1) investors can borrow and lend at the risk free rate and 2) unlimited short selling is allowed with full access to short sale proceeds. If these assumptions don’t hold, then the market portfolio might lie below the efficient frontier and the relationship between expected return and beta might not be linear.
So in one reading it says short sales lead to efficient frontier instability, but in another it says that unless short sales are allowed, the CAPM leads to inefficient results. Is there a discrepancy here or am I mixing apples and oranges?

YouCanDoIt

that’s a decent explanation, thanks. basically, im taking it to mean that shortselling creates reliability issues, which is why you want to prohibit short sales from the minimum variance frontier) in order to “trust” your variables more. but true equilbirium can only be reached with the shortselling, and the CAPM beleives that everything is in balance therefore it encourages shortselling.

Howd

One is practical, the other theoretical. Apples and oranges.
CAPM requires that short-selling be allowed (actually I think it requires that either unlimited short-selling be allowed OR investors can borrow at the risk-free rate in unlimited quantities - the CFAI text suggests that either condition can be met, Schweser says both must be - I queried this on AF, but was ignored!). That’s the theory.
However, were a portfolio manager to implement the minimum-variance portfolio, using weights spat out by his machine, he would find that there was an “overfitting” problem, because the machine is indifferent to going long or short it can suggest extreme short positions, based on very tenuous, sensitive predictions. Fiddle with these variables slightly and it will spit out a radically different answer. In the absence of perfect forecasting (of variables, I mean, as in expected returns and deviations - not actual returns!), the PM would prefer a more stable, and also less short-oriented (potentially volatile, sensitive to errors) allocation, so he restricts short-selling at the input level.
In other words, with reliable inputs: go with the manic short-heavy solution - that’s consistent with CAPM theory. If you’re less sure about the inputs, given their reactive nature, settle for a less risky portfolio (Note: the risk in question is MODEL risk, not systematic risk, which the model is based on!).

genuinecfa

Made a thread on this yesterday.
I think the minimum variance frontier refers to assumptions they take to reduce the number of imputes need to come up with the frontier. They limit short sales because the inputs change to much leading to the frontier being not stable.
Seems stupid, I know, just memorize and move on…