# Efficiency Frontier and Short Selling

From another post: “What would be the effect on the stability of the minimum variance frontier if short-selling was prohibited?” I’m not sure why it would change the “stability” of the curve… The combination of portfolio would run from asset A to asset B without going any further, but I cannot see why the shape of the curve between those two assets would change… I trust someone will correct me if I’m wrong…?

I don’t know what they mean by stability here, but the minimum variance frontier surely changes if you can short stuff. If you flip the sign of the expected return of a stock on the frontier, it (probably) drops off the frontier. Restore the sign (i.e., by shorting it) and it comes back.

Page 373, Reading 68 of last year’s level 2 cirriculum talks about it. Instability refers to when small changes in input assumptions leads to large changes in the minimum-variance frontier. It says “Responses to instability include the following: 1) adding constraints against short sales…” The reason it gives is that short selling has the potential to overfit mean-variance optimization.

“Overfit mean-variance optimization?” Is that english? Joey: Woulden’t that depend on the stocks… If they are perfectly negatively correlated, then one would think that you can make you’re frontier work fine… If they are perfectly positively correlated, you could short one to create an edge… Just sounds like it would depend on the stocks… But this isn’t my speciality…

It sounds like english to me, makes sense to me, and is a direct quote from the CFA text, so my answer is…yes.

Ok. Perhaps you could enlighten me to the meaning on this sentence…?

Sure…basically it is using statistically insignificant estimates for inputs to the mean-variance optimization framework. We must estimate expected returns, correlations, variances, etc…and when we do so using historical data that may have strong negative weights due to large short positions, that data can become insignificant and meaningless.

johnnyblazini Wrote: ------------------------------------------------------- > Ok. Perhaps you could enlighten me to the meaning > on this sentence…? You can see that if you try running a few optimizations in Excel using Solver. I put together an example: Instrument 1 2 3 4 ExcessRet 12% 12% 15% 15% Weight 3% 47% 24% 26% ExcessRet 12% 12% 16% 15% Weight -16% 60% 41% 16% ExcessRet 12% 12% 14% 15% Weight 22% 35% 7% 37% For all of the above: StDev 12% 12% 15% 15% Correl 1 0.8 0.6 0.3 0.8 1 0.3 0.3 0.6 0.3 1 0.7 0.3 0.3 0.7 1 It’s easy to see that even relatively small changes of inputs cause very significant changes of optimal portfolio weights.

to almost quote the big lebowski, “don’t F with the maritikus…” either way, was on last year’s test. pick some new random 1 paragraph this year in the 300 pages of PM to choose 6 questions on. i’d put money that they don’t get close to the min variance frontier this time. ICAPM would be too obvious. something painfully nitpicky about APT? factor models?

johnnyblazini Wrote: ------------------------------------------------------- > “Overfit mean-variance optimization?” Is that > english? > > > Joey: Woulden’t that depend on the stocks… If > they are perfectly negatively correlated, then one > would think that you can make you’re frontier work > fine… If they are perfectly positively > correlated, you could short one to create an > edge… Just sounds like it would depend on the > stocks… But this isn’t my speciality… That was the ‘(probably)’ in my answer. Perfectly correlated stocks wreck everything. Anyway, I don’t know what to say about limiting short sales increases the stability of mean variance optimization. I guess restricting weights to be within 1% of equally weighted increases stability too. I would say it restricts the solutions you can choose but does nothing to the underlying stability. “Increasing the stability” to me means something like getting less correlated stocks that have different leverages or something. Maratikus’ fine example above is unstable because those stocks all “look” about the same to the optimizer. If they are all the same, then all solutions are roughly as good.

bannisja Wrote: ------------------------------------------------------- > to almost quote the big lebowski, “don’t F with > the maritikus…” > > either way, was on last year’s test. pick some > new random 1 paragraph this year in the 300 pages > of PM to choose 6 questions on. i’d put money > that they don’t get close to the min variance > frontier this time. ICAPM would be too obvious. > something painfully nitpicky about APT? factor > models? They had 6 questions on this topic?

Ya, the word “stability” is still throwing me off…

Five questions on this, and one question on ICAPM. That was the entire PM section. Zero questions on Treynor-Black, zero on APT, zero on currency exposures, etc…Very frustrating for those who read hundreds of pages and saw no questions relating to what we read.

johnnyblazini Wrote: ------------------------------------------------------- > bannisja Wrote: > -------------------------------------------------- > ----- > > to almost quote the big lebowski, “don’t F with > > the maritikus…” > > > > either way, was on last year’s test. pick some > > new random 1 paragraph this year in the 300 > pages > > of PM to choose 6 questions on. i’d put money > > that they don’t get close to the min variance > > frontier this time. ICAPM would be too obvious. > > > something painfully nitpicky about APT? factor > > models? > > > They had 6 questions on this topic? Johnny: That’s why there was a response on the "Not finding level II so difficult… " thread - the material’s not bad. But the test, she is a nasty, nasty beech.

> Johnny: > > That’s why there was a response on the "Not > finding level II so difficult… " thread - the > material’s not bad. But the test, she is a nasty, > nasty beech. I can see that…

regardless of correlations (vs other asset class), if you introduce an active extension (130/30 for example) “asset class” you will effectively shift the frontier up and to the right since 130/30 products simply have lower standard deviations compared to other asset class. with the benefit of negative correlations (in the correlations matrix vs other asset class), you will definitely see an improved frontier shift. then again, with the recent market turmoil and the instability of 130/30 products (they have actually done worse than domestic equities/ broader market), we have seen an increase in volatility over the recent 15-18 months. then again, most active extension have a slight higher kurtosis than most long-only products (and pure short-selling products have the worst sharpe ratio, relative to other hedge fund strategies, and significant leptokurtosis) so a mean-variance approach to the optimization will definitely bias your variance downward; that is, your new frontier looks better than what it “should” be.