Let's say that we expect a stock that's been going up over the past week to now go down, since traders are expected to book profits and the price will accordingly decrease. Our trading universe has only 2 stocks - Google and Apple. We could have a trading strategy in which our position in a stock is given by

position $= - ($past week return$)$.

Using the above, we get positions in Google and Apple as $+2.5$ and $+7.5$ respectively. So far so good. Now, suppose we're expecting some bad event for the technology sector. A long position in these stocks could result in heavy losses. The book prescribes that one way to avoid such losses is to develop a sector-neutral strategy - the sum of positions of individual stocks in that sector would be $0$, i.e., take a long position in either Google or Apple and an equal short position in the other.

"This would change the old values of $+2.5$ and $+7.5$ to $-5.0$ and $+5.0$ for Google and Apple, respectively."

I can understand that we go long in Apple since our previous strategy prescribed a higher positive position in it ($+7.5$ as against only $+2.5$ for Google). But we could just as easily have had a different prior strategy that similarly assigned a more positive position to Apple. So the end result would've been similar - a sector neutral strategy that assigns $+x$ to Apple and $-x$ to Google.

In that sense, doesn't the sector-neutral strategy make our previous trading strategy completely irrelevant (apart from the magnitude of $x$)?

• I am not an expert in this field but I suppose there is some information missing to give a meaningful answer to your question. Could you be more precise in describing how the initial positions are derived? – muffin1974 Feb 7 '17 at 12:16
• @muffin1974: We look at the historical data for the 2 stocks (in this case, the past week's price data). Then we calculate the weekly return for each stock. The positions are calculated on a relative basis, that is, weekly return for G and A are 2.5% and 7.5% respectively, so we simply assign them positions 2.5 and 7.5. If we had USD 10 mil to invest, we'd invest USD 2.5 mil in G and USD 7.5 mil in A. – u23 Feb 7 '17 at 12:29

One thing you could do is make your trading signal sector neutral. For example, you can z-score your signals within each sector. For your example, your signals would be transformed from $(2.5,7.5)$ to $(-1.0,1.0)$. Your portfolio construction methodology is to take weights directly proportional to the signals, so in this case, having symmetrical weights makes sense. If you have more stocks, the signals will be transformed differently, for example $(2.5, 4.0, 7.5)$ is transformed to $(-1.03, -0.32, 1.35)$. Now you can see the situation is not symmetrical, and the strong signals are penalized less than the weak ones. So the information of your strategy is not 'lost' under the ranking operation.

An alternative would be to think of different ways to construct your portfolio. For example, you can think of explicit sector weight constraints in a Markowitz type optimization.

• Could you please explain how $(2.5, 4.0, 7.5)$ got transformed to $(-1.03, -0.32, 1.35)$? I'm not familiar with the concept of Z-scoring. Are there any other techniques apart from Z-scoring that would preserve the strength of the original weights and yet result in new weights adding to $0$? – u23 Feb 10 '17 at 13:17
• @ShirishKulhari, the z-score is defined as $\frac{\text{Signal}-\text{Mean Signal}}{\text{Standard Deviation of Signal}}$. For example, the mean of $(2.5, 4.0, 7.5)$ is $\sim4.67$ and the standard deviation is $\sim2.10$. So $2.5$ is transformed to $\frac{2.5-4.67}{2.10}=-1.03$. If you want the sector weights to sum to 0, you can try the optimization suggested by madilyn. Alternatively, you could try a Markowitz optimization where you have tight constraints for all sector weights, for example they should be in $[-1\%,1\%]$. – Comp_Warrior Feb 10 '17 at 16:19
• Oh okay. I was confused at first because I was using the same formula but with the sample standard deviation. – u23 Feb 10 '17 at 16:26
• Z-scoring seems to be useful if all the weights in the vector represent the same sector stocks. If we have some vector with $4$ entries - $2$ for one sector and $2$ for another, we could apply Z-scoring to the individual vector subsets. But then how do we account for the relative strength of the signals for the $2$ industries? For example, our original vector may be such that more weights (stronger signals) were assigned to one industry as compared to the other. – u23 Feb 10 '17 at 16:34
• @ShirishKulhari If you start to account for the relative strength of two industries, can you still talk about an industry neutral strategy? Because then you are actually saying that you want explicit industry tilts. The whole point of ranking within industries/sectors is to avoid taking these tilts, and hence have an industry/sector neutral strategy. – Comp_Warrior Feb 11 '17 at 1:47

Yes, your initial strategy would be rendered irrelevant since all that is saying is that you constrain

$w_1 + w_2 = 0$

and so your solution is undefined if $w_1,w_2>0$. One way you could make your strategy useful under a sector-neutral constraint is to change it into an optimization that minimizes the differences between actual weights and unconstrained weights, subject to the above constraint. e.g. Find

$\underset{w_1',w_2'}{\min} \left(w_1'-w_1\right)+\left(w_2'-w_2\right)$

subject to

$w_1 + w_2 = 0$