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Market Neutral Trading Strategies — Transcript

by Roman Paolucci · 5,389 words · 821 segments · language en · Watch on YouTube

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0:00You shouldn't have to wait to get to a
0:01desk at a bank or a hedge fund to
0:03understand how all of the pieces of the
0:05puzzle fit together. The bigger picture.
0:08This is one of the failures of academia.
0:12We learn about diversifiable risk,
0:14undiversifiable risk, pricing models,
0:17CAPM, FMA French extensions. We may even
0:20corroborate that theory with
0:21unsupervised learning, principal
0:23component analysis. The list goes on.
0:26But how do we use it to make trading
0:30decisions? What is all of that theory
0:33actually used for? You shouldn't have to
0:35wait to get to the desk to understand
0:38how all of the pieces of the puzzle fit
0:40together. That's exactly the purpose of
0:41today's video. We're going to talk about
0:43the mathematics of market neutral long
0:45short strategies so we can see exactly
0:49how all of the pieces of the puzzle fit
0:51together before you even touch an
0:54institutional desk. It all starts with
0:58this notion of diversifiable and
1:00undiversifiable risk. What is the
1:03difference between the two? Well, one
1:06you can get rid of very easily. The
1:08other one you got to be a little bit
1:10more creative. All right, that is the
1:13too long didn't watch. What exactly do I
1:16mean by that? If you approach a
1:18portfolio of risky assets, you can think
1:21of bonds, you can think of stock, you
1:23can think of crypto, alternative assets,
1:25whatever, there are going to be facets
1:28of risk in that portfolio that you
1:30cannot diversify away. You cannot remove
1:33by simply holding more risky assets.
1:37That is the systematic risk component,
1:39the undiversifiable risk component. And
1:41that is exactly what this animation here
1:44depicts. You can see as we increase the
1:46number of assets in our portfolio,
1:49you're going to see that the overall
1:51portfolio risk is going to decline until
1:53we hit this floor. And this floor is
1:56known as the systematic risk, the
1:58undiversifiable risk. We've effectively
2:00diversified away, removed the
2:03diversifiable risk by simply holding
2:06more risky assets in our portfolio. If
2:10you're familiar with portfolio
2:12optimization and the bullet curve, this
2:14is the idea of arbitrarily increasing
2:16your sharp in sample, pushing out that
2:18curve. It is the only free lunch in
2:23economics. Now, of course, when we
2:26approach this undiversifiable risk,
2:28right, we are holding this equity. So,
2:31why would we ever do that? Why would we
2:33be willing to hold this undiversifiable
2:35risk at all? Well, on average over a
2:39long enough time horizon, we are to be
2:41compensated for bearing that risk.
2:43Otherwise, nobody would do it, right?
2:46That is exactly what it means to bear
2:49this type of exposure. This is pretty
2:52much what every wealth advisor
2:54retirement account looks like. It's just
2:56bearing this exposure because what? Over
2:58a long enough time horizon, you're going
3:00to be compensated for bearing that risk.
3:02You'll have an iron stomach in your 401k
3:05or your Roth, whatever it is, and simply
3:08you are being compensated over a long
3:10enough time horizon for holding the
3:12market portfolio, bearing this
3:14systematic risk. Maybe that looks like
3:16holding VU, maybe SPY, whatever. But you
3:21can't diversify that away. When you hold
3:23those ETFs, you're already holding a
3:26diversified portfolio. So when you have
3:29massive equity drawdowns or any sort of
3:32crash or bare cycles right that is you
3:35effectively right going on a diet right
3:38it's an unpleasant experience but the
3:41upside is yet to come and in the
3:43retirement sense you have plenty of time
3:46to wait it out for that upside now all
3:49of this of course is just theory and
3:52you're always subject to risk you know
3:54in retirement what if you have a crazy
3:57100year crash cash. Yeah, welcome to the
4:00party, right? That would suck. So, this
4:02is the difference between diversifiable
4:05and undiversifiable risk. This is an
4:07abstraction still. Really, we should be
4:09slicing up the diversifiable risk into
4:12different components along with the
4:15undiversifiable risk. We should have in
4:18the factor sense, right? Market risk
4:20premium. We should have maybe in the FMA
4:22French sense small minus big, high minus
4:24low. all of these different
4:26undiversifiable
4:28risk slices that our portfolio is
4:31exposed to. But we're going to build to
4:33that so that we can actually understand
4:35this broader notion of being market
4:37neutral. Because right now, if we hold a
4:40significant number of assets in our
4:43portfolio, we are not market neutral. We
4:46are quite literally bearing that market
4:48exposure. That is what the
4:50undiversifiable or systematic risk
4:52exposure is. Okay, what does this look
4:56like in the portfolio sense? This
4:59picture is great. It's it's a classic in
5:02the classroom, but what does it actually
5:04look like? That's what we're going to
5:06see here. I want to start by showing you
5:08what I mean by idiosyncratic or
5:11diversifiable risk exposures. We're
5:13going to take a look at the SPY ETF, the
5:16S&P 500 ETF proxy, and individual stock
5:19paths here. What you're going to see is
5:22the individual stock paths are all going
5:24to have their own individual
5:26realizations. Clearly, this is probably
5:28AMD, Nvidia, Broadcom, whatever. These
5:31outperformers here, we even have some
5:33underperformers here. And in the broader
5:36sense of being compensated for bearing
5:40risk, you are not compensated on average
5:43in the cross-sectional sense for bearing
5:46idiosyncratic or firm specific risk
5:49exposure. That is diversifiable.
5:52All right. Is it true that you can go to
5:55the casino, bet your entire portfolio on
5:58any one of these sample paths? Yes, you
6:01always can do that. But in the actual
6:04sense of the literature, we're looking
6:06at in the cross-section on average what
6:09tends to be the case as a risk premia
6:12should you hold it over a long enough
6:13time horizon. There doesn't appear to be
6:16any evidence that bearing that
6:17idiosyncratic risk is compensated. In
6:20fact, volatility risk puzzle or not the
6:23volatility risk puzzle, the um
6:25idiosyncratic volatility puzzle suggests
6:28that you are actually losing value on
6:30average. And there are a lot of
6:32different things that might, you know,
6:33be attributed to that net effect.
6:35Lottery ticket effect. A lot of people
6:37are willing to fullport risky assets
6:39even if they aren't compensated on
6:41average over time because they don't
6:43know any better or they're willing to
6:46try to get this lottery ticket style
6:48payoff. Um, RSUs may have something to
6:50do with it. This is a very interesting
6:52subject for discussion. Um, and largely
6:55most likely a retail consequence. um
6:58because I guarantee you institutional
7:00institutions aren't bearing negative
7:02exposure over long time horizons. That's
7:05um quite literally insane.
7:07So here what you're observing now is all
7:10of these different idiosyncratic paths,
7:12right? So we're saying in the
7:13cross-sectional sense it's not worth
7:15bearing that exposure. And you see the
7:17S&P 500 path here. And it's kind of
7:20interesting, right? because all of these
7:21paths appear to echo in some shape, way
7:24or form this S&P 500, this spy ETF proxy
7:29path. All right, what happens if instead
7:32of looking at individual names, we
7:34diversify away the risk from individual
7:36names? Instead of looking at Nvidia,
7:38AMD, we look at chips. Instead of
7:40looking at Sigma, Etna, whatever, we
7:43look at healthcare, right? Let's
7:45compress all of these individual stock
7:48price paths, these individual stocks
7:50into now sector portfolios. So if we do
7:54this, we're going to get a new set of
7:56paths and it looks somewhat similar, but
7:59the extremes are certainly damped down.
8:03Of course, you're going to have chips
8:05significantly outperform over this
8:07sample. This sample goes back roughly 5
8:10years. And what we're seeing here now is
8:13if you look at the sectors, right, they
8:16echo the S&P 500 path, this yellow path
8:19here, even more, right? And what we're
8:23actually observing in action now is this
8:27idea of diversifiable risk approaching
8:31undiversifiable risk. So you can see
8:33here, diversifiable risk runs rampant.
8:38And then when we compress to sectors,
8:40we're starting to diversify a bit more
8:42and it's starting to converge to what?
8:45Well, what happens if instead of holding
8:47sector portfolios, we hold a giant
8:49composite portfolios of equally weighted
8:51sectors. So now instead of taking all
8:54the individual names, throwing them into
8:56sector portfol sector portfolios for
9:00financials, real estate, consumer
9:01staples, we're going to take all of
9:03those portfolios and hold an equally
9:05weighted version of that. Look at what
9:08we're left with here. We are left with
9:10an equally weighted portfolio of sectors
9:13relative to the S&P 500. And wow, it
9:17certainly does appear to track quite
9:20similarly. And this of course isn't by
9:22accident. This is the net effect of
9:25holding more assets in your portfolio.
9:28We literally went from diversifiable
9:30risk all the way down to undiversifiable
9:33risk. And this is what it looks like
9:36when you do that. The difference is
9:39almost net zero between these two paths.
9:42This is what your wealth manager is
9:44doing. and he probably doesn't even know
9:45that's what he's doing, but he's bearing
9:48exposure to this undiversifiable risk
9:51factor. And over a long enough time
9:53horizon, fingers crossed, by the time
9:56you get to retirement, there isn't a 80%
9:58draw down in your portfolio and you can
10:03generally have gained the benefits of
10:06bearing that exposure of over a long
10:08enough time horizon. But, you know,
10:10that's the the fundamental irony of the
10:12situation here is that's that's all
10:13they're doing. It's quite literally a a
10:16fingers crossed bet on that
10:18undiversifiable risk factor. All right.
10:23Nobody knows the direction that the
10:25market winds are going to blow, right?
10:28Maybe five years into your retirement
10:31account, there's a a nasty draw down.
10:33Maybe we even recover and exceed the
10:36previous high. But again, what have you
10:38done for me lately? Right? We would
10:40prefer to run more intricate strategies
10:43such that we're leaving less up to
10:45guesswork, right, by the time we reach
10:48that retirement age. But that's just one
10:50man's opinion. I would prefer not to
10:52stake my life savings on a fingers
10:55crossed bet on undiversifiable risk
10:59exposure.
11:00I'll digress for now. Right. What is
11:04actually in the data sense based on
11:06everything that we've seen at least here
11:09so far suggesting that this
11:12undiversifiable risk factor even exists.
11:15[snorts]
11:16This is where we can start to do a
11:18principal component analysis. And this
11:21is where things get pretty interesting.
11:23So we have this theory here and the
11:25theory is great but does the data
11:28corroborate it? Well, for the most part
11:29based on everything we've seen, yes. Is
11:32there anything else we can do to go into
11:34the data and let it speak for itself?
11:37Well, certainly there is. And that is
11:39this broader notion of compression and
11:42observing a new basis for our return
11:46data. What we're going to do is take a
11:49look at a panel of returns and
11:51diagonalize the coariance matrix. In
11:55doing that, what's going to happen is we
11:57are going to get new components
12:00that express the maximum amount of
12:03variation explained for a specific
12:05direction orthogonal to all other
12:07directions until we accumulate 100% of
12:09the variance in the data. What does that
12:13look like visually? Well, let's take a
12:15look at what we got going on here.
12:17Assume these points, this scatter plot
12:20is return data. What we're going to do
12:23is plot that return data and we are
12:26going to con construct effectively the
12:29coariance matrix and then work to
12:31diagonalize it. What does that mean?
12:33Well, we are going to start with the raw
12:35data. We'll center it and then we are
12:37going to perform an igen decomposition
12:40of the coariance matrix or a principal
12:42component and I'm sorry a singular value
12:44decomposition of the data matrix. And
12:47once we do that, we will have the igen
12:49vectors or the loadings that will
12:51produce the transformation required to
12:52yield these new principal directions.
12:56And what's actually going on here is if
12:58we take a look at the new principal
13:00component basis, we are seeing that
13:02principal component one is the direction
13:04that explains the maximum amount of
13:06variation in the data orthogonal to then
13:10the next the next component and the next
13:12component. So on and so forth. And what
13:14you're seeing here on the right is the
13:16amount of variation that each component
13:20explains. So principal component one
13:22here explains 94% of the variation in
13:25this particular sample. Now this is a
13:28synthetic sample. So these aren't real
13:30returns. You're observing an
13:32extraordinarily sharp spectral decay.
13:35You can see that the second component
13:37explains 5% of the variance. If we were
13:40to compress, we would not be throwing
13:41out all that much data at all. And by
13:45data, I mean in the information loss
13:47sense, in the compression sense. So if
13:50this is what we're doing, how are we
13:53doing it? Well, we need to find the igen
13:56vectors and the igen vectors are going
13:58to be the loadings that produce that new
14:02basis. So this animation here is showing
14:04you the construction of these loadings
14:07as a linear combination. So we observe
14:10these igen vectors. We see igen vector 1
14:13produces these two loadings. Igen vector
14:152 produces these two loadings. The
14:17linear combination on the original
14:19feature or return set is then going to
14:22produce the new basis and that is what
14:26you are seeing here. You're seeing now
14:28not the original feature one feature 2
14:30or time and returns. You're seeing PC1
14:33and PC2
14:35and this new scatter plot here that is
14:38effectively centered on these new axes.
14:42The efficacy of a principal component
14:44analysis is always subject to its
14:46stability over time. There's no reason
14:48for it to remain stable. You're subject
14:50to model risk just like everyone and
14:52everything else. There's no reason for
14:54it to converge. You're not drawing iid
14:56samples. We're dealing with the real
14:58world here and there's nothing that we
15:00can do to get around that. All right.
15:03But what happens now if we apply this
15:05methodology, this diagonalization of the
15:08coariance matrix again via SVD of the
15:11data matrix or decomposition of the
15:13coariance matrix to a real set of
15:16returns. Well, let's take a look at what
15:19happens when I run the principal
15:22components analysis on a panel of stock
15:24returns. I'm going to take a look at the
15:26variation explained via each principal
15:29component. All right. And what you're
15:31seeing here is the first principal
15:32component across a very large sample of
15:36assets. In this case, we have a 100
15:37stocks across different sectors. It
15:40explains 20% of the variation in that
15:44panel. Now, we're not observing nearly
15:46as sharp of a spectral decay here. And
15:49it's going to be sample dependent. It's
15:51going to be certainly dependent on the
15:53assets that you're selecting within that
15:55sample. And what we're essentially
15:58saying here is if the spectral decay
16:00isn't sharp, then the compression to
16:02that initial principal component isn't
16:04going to be as effective. What I mean is
16:07you require more information. You can't
16:09compress effectively into this one
16:11component. You require more information.
16:13You have far more information loss if
16:16you are to pitch out than in the
16:20dimensionality reduction sense the
16:23latter or the later principal
16:25components.
16:28How is this useful at all? All right,
16:30that just sounds like a lot of math for
16:31no reason. Well, it's not a lot of math
16:33for no reason. It literally is
16:35corroborating everything that we've been
16:37discussing up until this point. What do
16:39you think is dominating the variation
16:41explained in a panel of returns? It
16:44should not be a shock that that is the
16:46exact same undiversifiable risk
16:48component that we observed here as we
16:50went from individual stock to sector
16:53portfolios to holding a portfolio of
16:55sectors in the same way that we saw it
16:58in this animation here going from
16:59diversifiable to undiversifiable risk.
17:02The data is literally speaking for
17:04itself in the most intricate and
17:08largely unsupervised sense possible that
17:12that undiversifiable risk components is
17:15a principal source of variation across
17:17this entire panel of risky assets. Okay,
17:23the evidence gets even more
17:28the evidence gets even more interesting
17:31when you take a look at the IGEN vector
17:32loadings across the equity universe. On
17:36average, and of course sign is arbitrary
17:38in the IGEN vector sense, but on average
17:41the loading value is positive across all
17:44of these different stocks, across all of
17:46these different sectors. Sure, sometimes
17:47you're going to have idiosyncratic under
17:49or out performance dominate a
17:51trajectory, but largely on average all
17:55of these names carry the same magnitude
17:59or the same direction of risk. And that
18:02is exactly what you would expect from a
18:04portfolio bearing this undiversifiable
18:08risk exposure. Look at what happens in
18:11the individual names. This literally is
18:14exactly what is producing that principal
18:15component analysis that we just
18:17observed. We can see some names, right,
18:20are going to load very heavily on that
18:23undiversifiable risk factor, the market
18:27factor. Some names are going to
18:29idiosyncratically outperform. Some names
18:31are going to idiosyncratically
18:32underperform. Even in the sector sense,
18:34we see this. But with a large enough
18:37diversification, we are matching that
18:40component. And when we look at
18:42individual names in the principal
18:43component sense, this is exactly what we
18:46see. Now, isn't as sharp of a spectral
18:48decay here, meaning that the
18:50idiosyncratic or industry and and all of
18:52those other diversifiable components are
18:54also going to contribute to a
18:56significant amount of variation within
18:58the cross-section that is sample
19:00dependent here. And that is just the net
19:02effect. But even still that first
19:05principal component is dominating a
19:07significant amount of variation across
19:09this entire panel of returns. How do we
19:12quantify this and what is the
19:14significance of this? Well, if you want
19:16to make a bet on Nvidia, you are
19:18effectively carrying undiversifiable
19:20risk and diversifiable risk. So when you
19:24make that bet on Nvidia, what if Nvidia
19:26tanks? Well, if Nvidia tanks altogether,
19:30right, was that because Nvidia is
19:33underperforming or is it because the
19:36market is in the middle of a crisis?
19:39Right? You're just trying to make a bet
19:40on Nvidia. You don't want to say
19:43anything about the broader market. That
19:46is fundamentally the problem that we are
19:49approaching and the problem that we're
19:50going to use everything that we just
19:53discussed to quantify and solve. If you
19:57want to make an isolated bet on a name,
20:00a set of names, a trading signal, a
20:02strategy, you are carrying also
20:07that undiversifiable risk. That may not
20:09be your intention. That may not be your
20:12intention at all and you want to hedge
20:13that away. But how do we do that? I'm
20:15going to show you how to in quite a
20:17trivial sense using the capital asset
20:19pricing model. If we take a look at the
20:22capital asset pricing model, we can see
20:24that the assumption is that there is no
20:26alpha. We're saying that a portfolio or
20:30a a risky portfolio, a a universe of
20:33risky assets that is going to be
20:37constructed into a portfolio in some
20:39shape, way or form via a trading signal,
20:41via um equal waiting, uniform waiting,
20:43market cap, whatever. uh is going to
20:46effectively just be in terms of the
20:48expected return the risk-free rate plus
20:51beta multiplied by this excess market
20:54return here the market risk premium this
20:58is quite literally
21:01the undiversifiable risk here all right
21:04this is one slice of the undiversifiable
21:06risk as factor models have evolved over
21:08time but even still this is sufficient
21:12to tackle what it is we are trying to in
21:15the market neutral strategy construction
21:18sense because if we can measure our
21:20exposure to the broader market and if
21:22it's reasonably stable then we should be
21:24able to hedge it away and isolate a
21:27specific bet. All right,
21:31what does this actually look like? the
21:33CAPM model itself. I have this animation
21:35for you here of Nvidia versus the spy,
21:38healthc care versus the spy and an
21:40equally weighted portfolio of sectors
21:43versus the spy. When we look at Nvidia,
21:46we can see that there is significant
21:49covariance with the market. Beta is
21:522.17.
21:54And what that means is when the market
21:56moves up one point on average we expect
21:58the magnitude of the move of Nvidia to
22:00be 2.17 all else equal whatever
22:03in the CAPM model sense it's a very
22:07volatile asset relative to the market
22:09but I don't want to make a bet on the
22:11market. I want to make a bet on Nvidia.
22:13That's a a very fundamental concept
22:16here. If we're trying to trade some sort
22:18of market neutral strategy and yes, it's
22:20going to be in the cross-section and
22:21yes, it's going to be relative to more
22:23sources of undiversifiable risk and
22:25maybe even a particular factor you're
22:27targeting in a smart beta sense or some
22:29sort of alpha that you actually want to
22:31isolate relative to other model risk.
22:32But we're not talking about that right
22:34now. We're talking about CAPM just as a
22:36trivial example of this. Nvidia is going
22:39to bear the most what diversifiable risk
22:41exposure, right? So it's extremely
22:43volatile. That's what makes it carry
22:46more portfolio risk. Shocker. That's
22:48what we see here. If you're holding one
22:50name, you have significantly higher
22:52portfolio risk. Hence, significantly
22:54more volatility in the CAPM M sense.
22:58Okay. Then you go to a sector portfolio.
23:00Let's take a look at healthcare. All
23:02right. Well, healthcare now is going to
23:05bear what? It's going to bear
23:07significantly less volatility,
23:09significantly less portfolio risk
23:11relative to holding an individual name.
23:13And that's what we see here. We see beta
23:15is 0.24.
23:17It's 0.24.
23:19All right. So the net exposure to that
23:21undiversifiable risk is in sample less
23:25than one. All right. That means you're
23:28not going to be compensated as much on
23:30average. Then if you take a look at an
23:32equally weighted portfolio of sectors
23:35relative to the S&P 500, we have 0 71 in
23:38sample. Of course, this is largely going
23:40to be more relative to a beta of one.
23:43This equally weighted portfolio of
23:45sectors is the closest thing that we
23:46would have to just holding the S&P 500
23:49proxy for that market risk premium just
23:51like you see here. All right. So all
23:56that is to say is if we now have a way
23:59to quantify the exposure of a asset, a
24:03set of assets, a portfolio to this
24:06undiversifiable risk component. Then
24:09what can we do? Well, we can construct
24:12then a portfolio of offsetting legs,
24:16right? What if I want to be netneutral
24:20beta? What are the implications of that?
24:23Well, again, if I want to make a bet on
24:25a specific strategy, I don't want to
24:26make a bet necessarily implicitly on
24:29undiversifiable
24:31risk. That's not the objective of my
24:33model is to predict the macroeconomy
24:36direction. No, it's instead to forecast
24:39a very specific component of the
24:42portfolio. And that is the implication
24:44of being directional versus market
24:46neutral in this undiversifiable or
24:49systematic sense. On the left here,
24:52you're going to see what happens if you
24:54are directional in beta for your
24:57portfolio and you have a bull market.
25:01You can see, all right, we're highly
25:02directional. That's effectively what
25:04we're seeing here in the undiversifiable
25:06risk sense. We are directional to that
25:09undiversifiable risk. The market goes up
25:11on average, Nvidia goes up. The market
25:13goes up, on average, healthcare goes up.
25:15The market goes up on average the
25:17equally weighted portfolio of sectors
25:18goes up. And yeah, that's what we see
25:20here. If we have a very high beta, on
25:23average, our portfolio will increase
25:25when the market increases. On the right
25:29here, we see the subsequent the
25:31subsequent consequence of that. If the
25:33market underperforms, then we are going
25:35to severely underperform. All right,
25:37that is literally what it means to be
25:40bearing this undiversifiable risk here.
25:44That's literally what it means. When the
25:47market outperforms, you are going to
25:48perform or outperform depending on the
25:51volatility of your portfolio, the
25:53coariance with the broader market.
25:56And if it underperforms, no free lunch.
25:59That's literally you going on a diet,
26:02right, for downstream consequences that
26:04you hope are beneficial.
26:07Okay, that is the net effect of this.
26:10That is the net effect of CAPM and that
26:13is the net effect here. So why would we
26:14bother being market neutral? Well, I'm
26:17confident that my model is correct in
26:19that Nvidia is going to outpace AMD, and
26:21I want to make that bet. I'm not
26:23confident that Trump is going to pick up
26:25the phone and piss off China, right? And
26:29then the entire market's going to panic
26:31and and whatever, right? So, I don't
26:34want that exposure. I want my model
26:36exposure to Nvidia and AMD, right?
26:41That is how you isolate alpha. All
26:43right? That is how you remain market
26:45neutral. What you're observing here now
26:47is the net effect of this. On the left,
26:48you're seeing if you retain directional
26:50exposure, then yeah, the market goes up,
26:52your portfolio goes up. That's great.
26:54But on the right here, if we're market
26:56neutral and our model is correct about
26:57Nvidia and AMD, it doesn't matter what
27:00the market does. It can go up, down,
27:01sideways, left, right. There's no
27:03correlation. There's no covariance or at
27:04least we're targeting a net zero
27:07coariance with the broader market. The
27:09undiversifiable risk here. All right?
27:12We're not diversifying it away. In fact,
27:15we are just targeting neutrality. It's
27:17going to be time varying. It's going to
27:19change over time and it's going to be
27:20quite painful rebalancing or targeting
27:23rebalances to accomplish that. So, it's
27:26an empirical question largely to see how
27:28stable it is over time, whatever factors
27:32we are trying to neutralize in a
27:34particular strategies portfolio. Okay.
27:37But that is the the net goal. The net
27:40goal is to construct this market neutral
27:43portfolio to isolate specific alphas or
27:45idiosyncratic bets so that we can be
27:49market neutral. Okay,
27:53how do we do this? What does it actually
27:56look like to construct a market neutral
27:57strategy?
27:59Well, I've painted you a picture here
28:02with broad strokes. Step one is to
28:05develop a strategy pairs trade. You
28:07built a model you really like
28:09cross-sectional signal. Step two, proxy
28:12your exposure. Select a model. CAPM
28:15extensions.
28:16Step three, select your notional
28:18exposure. Are you dollar neutral? Right?
28:20What is your net exposure? 800, 700,
28:23450, 300. Step four, rebalance as
28:26necessary because your proxy is going to
28:29change over time. Let me give you an
28:31example of a market neutral strategy
28:34construction. And I actually have the
28:35empirical returns here. My model says
28:38Coke will outperform Pepsi. All right.
28:40Now I must isolate this bet. And in the
28:42Paris trading sense, you know, we would
28:44expect maybe the coariance of Coke with
28:46Pepsi to be roughly similar with the
28:49market. So when we come up with that
28:51hagged ratio, we're implicitly beta
28:54neutral. And you're going to see what I
28:55mean in a moment. I'm going to proxy for
28:57my undiversifiable risk exposure using a
29:00pricing model here. CAP M for
29:02simplicity. I'm going to be dollar
29:04neutral. Um maybe targeting dollar
29:06neutral. So equal long short capital and
29:09hedge the undiversifiable exposure. Um
29:12again assuming that they are roughly
29:13equivalent to the coariances of each
29:16other with spy. And then four I'll
29:18rebalance quarterly or as necessary
29:21since the coariance is certain to change
29:22over time. So here's my isolated bet on
29:25Coke and Pepsi. What you're observing on
29:28the right here is the X anti-BA
29:30and the realized beta. And what's really
29:34interesting about this is you're seeing
29:35the short Pepsi leg here. You're seeing
29:37the long Coca-Cola leg. You're seeing
29:40the S&P 500 here. And you're seeing the
29:43net long short beta neutral pair. This
29:46green line. Now, what I want you to
29:48notice is if I isolate just the green
29:50line with the market, they have
29:54literally nothing to do with each other.
29:55Look, the market goes down here. My co
29:57my Coke and Pepsi bet goes up here. All
30:00right, that's not a mistake. That was
30:02the intention. All right, that is the
30:04intention. And I'm not telling you to
30:06copy this strategy. All right, I am
30:09telling you in the modeling sense, if
30:12you build a model, right, with the
30:14intention of targeting this exposure in
30:16a forward-looking sense, you have to
30:19target neutrality among all these other
30:21factors. they will otherwise dominate.
30:24They will otherwise dominate your return
30:26profile. So if you didn't when the S&P
30:29500 had a draw down here, right, and you
30:32weren't targeting beta neutral, right?
30:34And yeah, correlations go to one, it's
30:36going to be messy shorts, the real
30:37world, you wouldn't have this
30:39outperformance. That is the entire
30:41purpose of remaining market neutral.
30:43You're isolating the specific exposure.
30:46And then based on everything that I've
30:47ever talked about on this channel in
30:49terms of improving your sharp ratios, in
30:51terms of running a personal hedge fund,
30:53objectively in the volatility drag
30:55sense, if you have orthogonal exposures
30:58to idiosyncratic alphas, you are
31:00arbitrarily decreasing your portfolio
31:03variance, increasing your expected
31:05return, increasing your sharp ratio,
31:08increasing your keer, your geometric
31:09compounding. That is your objective.
31:12hedge funds, banks, whatever. You take a
31:15look at the way that they actually run
31:16capital. It's in pods on purpose. On
31:19purpose. It's by construction
31:20mathematically that if you have
31:22individual sources of orthogonal risk
31:25that are capable of producing net
31:28positive expected value over time, you
31:30are going to improve your risk return
31:32profile. And that is the entire point of
31:34running a market neutral strategy. So
31:38this is how all of the pieces of the
31:39puzzle fit together. We start from
31:42diversifiable undiversifiable risk. We
31:44take a look at what it looks like
31:45visually to compress to undiversifiable
31:48risk and then we take a look at
31:49principal component analysis as an
31:51unsupervised means of corroborating that
31:54theory. Then we take a look at the
31:56capital asset pricing model and
31:58extensions found by Frank other factor
32:00models factors use whatever to try to
32:02proxy in a quantitative way for what we
32:04need to neutralize. we see that oh wow
32:07if we run a market neutral strategy it
32:09doesn't matter what the broader
32:10macroeconomy does so long as our model
32:12is correct and then when we go about
32:15constructing that market neutral
32:16strategy here I show you on Coke and
32:18Pepsi in reality you would probably do a
32:20broader cross-sectional signal if you
32:21have significantly more data whatever it
32:23is you're actually trying to run you see
32:26the net effect when the market is down
32:28it doesn't matter so long as our model
32:30is correct and we've reasonably
32:32neutralized beta all right That is in
32:38roughly a half hour how all of the
32:41pieces of the puzzle fit together. Did I
32:45leave some stuff out? Sure. Would I like
32:47to go in more depth into the
32:49mathematics? Yeah. But nobody wants to
32:51watch that. All right. I've tried very
32:53hard. I do a lot of math videos and
32:56nobody wants to watch that. So, if you
32:58would like to watch it, let me know in
33:00the comments section below. I'd be very
33:02happy to selfishly make a video on the
33:05topic and we could talk even more. I'll
33:07break out the iPad and the the actual
33:09mathematics at play here, what it means
33:11by construction for these hedge funds
33:13for these hedge funds to run individual
33:15and orthogonal bets in this capacity.
33:19But that will largely be up to you guys.
33:23All right, that being said, that is
33:25going to do it for this video on the
33:28mathematics of market neutral long short
33:31strategies. All right, I hope you
33:33enjoyed. I hope you learned something.
33:35This video certainly took a tremendous
33:37effort to make. So, if you liked it and
33:38you want to see more like it in the
33:39future, please like, comment, subscribe,
33:41share. It helps me out tremendously. It
33:43is always greatly appreciated. Other
33:46than that, I'm going to thank you so
33:48much for watching and I'll see you in
33:51the next

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