Tony Battista: Thomas we're back my friend. Skinny On Options Math with Jacob in the house. Jacob you are wet, you are tired, you are bruised, you are battered, you got to get a car dude.
Tom Sosnoff: Like a wet dog, like a wet dog.
Jacob P: It was a rough commute this morning.
Tony Battista: I bet.
Jacob P: I knew I should have taken the CTA.
Tony Battista: Uh huh (affirmative).
Tom Sosnoff: Take the tastylive limo back please.
Jacob P: Alright, alright.
Tom Sosnoff: Yeah.
Tony Battista: Is this just a short trip? You don't need the jet?
Jacob P: No, no, yeah. The limo will be fine.
Tom Sosnoff: The limo is Tony's pickup truck and we'll just put the bike in the back, and we'll just …
Jacob P: That sounds perfect, yeah?
Tom Sosnoff: Yeah. We're going to be covering today, the Sharpe ratio. Now this doesn't have anything to do with like-
Tony Battista: Shannon Sharpe?
Tom Sosnoff: Shannon Sharpe, yes the Sharpie…
Jacob P: No, no.
Tom Sosnoff: What kind of dog do you have.
Jacob P: What?
Tom Sosnoff: What kind of dog do you have?
Jacob P: A Border Collie.
Tom Sosnoff: A Border Collie?
Jacob P: Yeah. Well mixed but yeah.
Tom Sosnoff: My son just got a Border Collie.
Jacob P: Yeah, how's he doing with it?
Tom Sosnoff: It's a puppy.
Jacob P: Yeah. It's a lot of time.
Tom Sosnoff: Yeah the Border Collie?
Jacob P: It's just all puppies and especially a Border Collie is … You got to spend a lot of time with them.
Tom Sosnoff: How do you like it?
Jacob P: He's good, though he has an ear infection right now and does not like me having to put stuff inside his ear.
Tom Sosnoff: You fool him. You do what we do with-
Jacob P: You do with Tony?
Tony Battista: Fool him like Tom does to me. He comes up from behind me, he puts his hand over my eyes and then puts it in.
Jacob P: Yeah. It's more or less… I have to hold him down and cover his eyes and put a treat in his mouth and the thing in his ear.
Tony Battista: Typically he has to hold me down too.
Jacob P: Yeah.
Tom Sosnoff: Yeah. You think you're funny but you're not funny. Sharpe ratio?
Tony Battista: Wait until you hear from my attorney.
Jacob P: Sharpe ratio, so no it's … Because it's a finance thing it has someone's name on it. It's William F. Sharpe, but in his defense, he didn't call it that. He called it the, reward to variability ratio.
Tom Sosnoff: I like that. The reward to variability.
Jacob P: That also explains what it is much better. I carry information by any other name because, throughout the rest of math, and statistics, and signal processing, there's an identical thing, which is called the information of a signal. The Sharpe ratio is under, sort of, what's more wide spread terminology, the information of the excess returns.
Tony Battista: Oh sure.
Tom Sosnoff: I don't think I've ever, have I heard it explained like that before? I don't think so. Yeah. The information of the excess returns. All right let's break that down. What is the Sharpe ratio? You're going to have to take this one.
Jacob P: Yeah, so the Sharpe ratio. The key thing here is the information of the excess returns, so the two things to understand are, what are excess returns and what is information. Excess return is pretty easy, you pick some benchmark, maybe T bills, maybe S&P, whatever, and you just look at given some other specific thing you might have, any sort of asset.
Tom Sosnoff: Would it be anything other than a risk-free return?
Jacob P: Sometimes it's a risk-free return.
Tom Sosnoff: No, anything other than a risk-free return.
Jacob P: For the benchmark or for the asset?
Tom Sosnoff: Yeah for the benchmark. Wouldn't the benchmark be anything but risk-free? Jacob P: You can use the risk-free return as your benchmark too, if you want, because it's just how much, what are your returns in excess of whatever your benchmark is and if your benchmark is risk-free, then it's a very simply computation for what are your returns in excess of it, but-
Tom Sosnoff: What do most people use as a benchmark?
Jacob P: S&P 500, I think is the most common.
Tom Sosnoff: What's that? I mean, what number are you using?
Jacob P: What do you mean?
Tom Sosnoff: I mean are you using S&P 500 for last year, for last 50 years? what is it? Jacob P: You have to pick a time period, and you're going to need to look at them over the same time period. There is, when looking at Sharpe ratios, deciding what time period to use it is important and particularly you don't want to try to compare Sharpe ratios that are across different time periods.
Tom Sosnoff: Okay I understand that. So I guess, to make this more valuable for me is it generally a long duration? Is it a short duration, and is it the S&P net?
Jacob P: It's returns not net. It's always log space, it's percent returns.
Tom Sosnoff: Percent returns.
Jacob P: It's percent returns.
Tom Sosnoff: So but it's net percent returns.
Jacob P: Right.
Tom Sosnoff: After fees and anything else?
Jacob P: You just have to do the same one for both of them. If you're going to compare your asset net, you should do your asset net and your benchmark net. If you want to do neither, if you want to do them both gross, you can do them both gross.
Tom Sosnoff: Okay got it.
Jacob P: Right, the important part is that you want to stick to an apples to apples. You want to be over the same time period, like a month or a year, and you want it to be the same net, either both net or both gross and it's in percent returns.
Tom Sosnoff: Got it. Okay.
Jacob P: Then you just look at, the excess return is the difference, right? However much you make more than whatever your benchmark is and…negative of course.
Tom Sosnoff: Sure.
Jacob P: Then the information of any sort of signal is the mean divided by the standard deviation. Which sort of gives you a good feeling for like, how much can you actually expect. How good is this mean. If the mean is real high but the standard deviation is also really high, then you might not get that much out of it. This is where reward to variability is the originally name for the ratio, which I think is much more explanatory.
Tom Sosnoff: Got it. Interesting.
Jacob P: Now both the returns are in percent, are in percents and the standard deviation, that square root of variance, is also going to be in percents. Which means that the ratio of the two of them is completely unitless. It's like an abstract number and which makes it possibly hard to interpret what a Sharpe ratio means. If someone comes along and tells you this thing has a Sharpe ratio of .05.
Tom Sosnoff: Yeah, like exactly, so I understand it's the average of the excess return divided by it's own standard deviation.
Jacob P: Yeah.
Tom Sosnoff: How do I put that into lay' terms? What am I looking for? If the Sharpe ratio is, what's the best Shape ratio you can have?
Jacob P: Higher, higher is better.
Tom Sosnoff: Higher is better.
Jacob P: Higher is better. Higher is better generally, there is a fact where if you're using S&P's as your benchmark, then you maybe actually want kind of a high standard deviation in your excess returns because that's a good sign of non-correlation. High correlation will result in a, a high correlation can result in a high Sharpe ratio.
Tom Sosnoff: Okay but who knows this? What I've seen is, before I've seen, I've seen people present different portfolio methods and things like that.
Jacob P: Right, and then they'll quote the Sharpe ratio there-
Tom Sosnoff: They'll quote the Sharpe ratio.
Jacob P: And no one asked them what that means.
Tom Sosnoff: That's exactly right.
Jacob P: That's what I want, I want to talk about what does this mean.
Tom Sosnoff: I said that's exactly where I'm going.
Jacob P: Yeah.
Tom Sosnoff: I only known that, okay, if it's higher it's better but then why would somebody quote their Sharpe ratio if it wasn't good?
Jacob P: Well maybe because everyone is expecting you to and also, there are some thing … If someone only ever quotes good Sharpe ratios to you, these are the things we're going to cover later, but if someone only ever quotes good Sharpe ratios that's one of those like big red flags for fraud investigators.
Tom Sosnoff: Yeah but how do you even, if someone quotes a Sharpe ratio, sounds to me like you can, without having all the … Without knowing the variables that went into that ratio-
Jacob P: If they don't tell you if they're net or gross, if they don't tell you the time period, then it really doesn't mean very much.
Tom Sosnoff: I've never seen anybody tell you any of that stuff.
Jacob P: Then you probably shouldn't trust them very much.
Tom Sosnoff: I'm saying, I've never seen people, so I'll get a proposal and it'll have, look at our Sharpe ratio it's 1.39 or whatever, okay.
Tony Battista: I guess that's awesome.
Jacob P: Yeah that sounds great.
Tom Sosnoff: I don't even understand the question, because people, listen you walk into an investment advisory, public, private whatever it is right now and you sit down the first thing they say is, look at our Sharpe ratio it's better than all our competitors, and I'm like , yeah but what does that mean?
Jacob P: Exactly.
Tom Sosnoff: I'm not sure and I want to explain that here.
Jacob P: Even if they're being fully above board and telling, and like not fudging with their time frames, and not fudging with their gross versus nets and fully above board. Then what it means to have, if they have a high Sharpe ratio, it means that they generally make more than the benchmark and that it doesn't vary that much.
Tom Sosnoff: Okay.
Jacob P: That's really what a Sharpe-
Tom Sosnoff: What is a high Sharpe ratio? Like anything positive?
Jacob P: Anything positive is good. You're going to be positive any time you're performing in excess of the benchmark. If you're doing better than the benchmark you're going to be positive, and then higher, if you cross one, I think in practice most thing are like .05 or something.
Tom Sosnoff: Okay so what I've learned on the first three slides is, and I know there's a million slides here and so we'll have to move forward, but what I learned on the first three is that; my take away is, that the Sharpe ratio, if I'm running my own business, my own advisory business or whatever it is, my prop firm and I have our own traders and we set whatever our benchmark is or our own advise, whatever it is, and we set our own benchmark then internally it's a extremely valuable asset. To see where somebody or bodies are doing good. Where they're adding value to the firm.
Jacob P: That's exactly, it's really hard to look at a Sharpe ratio in its abstract. You have to be really experienced with them to have some idea, but comparing them-
Tom Sosnoff: You have nothing to compare it to.
Jacob P: Side by side they work pretty well.
Tom Sosnoff: Right, of course.
Jacob P: You look at one you look at another.
Tom Sosnoff: So, internally, this is another reason why there's so much garbage in the world of finance because everybody, all you hear is Sharpe ratio, but the reality of the Sharpe ratio is if it's not measuring against something else or it's not explained, how do you even know what it is?
Jacob P: It's a really tricky thing. You could decide what you really want to do is become adept at the Sharpe ratio and then spend a bunch of time looking at various investments and sort of -
Tom Sosnoff: Who does that? Yeah.
Jacob P: Getting a feel for a .05 ratio is okay but not great and a .02 Sharpe ratio is a really good one. You would learn this but there's not a good way to have this come from-
Tom Sosnoff: The expected value and standard deviation may be computed theoretically from a model, the ex-ante.
Jacob P: So this is William Sharpe's fault that he chose this goofy terminology. Ex-ante and ex-post for theoretical and empirical.
Tom Sosnoff: What does that mean?
Jacob P: It just means, one is, so there's the expected value and the standard deviation in the previous slide and those can either be, if you have like a rigorous model, like we're working on Black-Scholes.
Tom Sosnoff: Okay.
Jacob P: You can compute those. You can get like a theoretical value for both of them and you get like a predictive chart value. Something before your ratio, before you do it, or you could look at people in house and to see how [inaudible 00:10:17] are these people doing, and then you look at their personal returns, and then you just plug those in and do it, expected value computation or standard deviation computation.
Tom Sosnoff: The length of the time period is important when comparing Sharpe ratios. Even if everything was perfectly regular, we would expect the Sharpe ratio to scale like, what the square root of time?
Jacob P: The square root of T.
Tom Sosnoff: The square root of T, and that's time right?
Jacob P: Yeah time.
Tom Sosnoff: Okay and since the mean scales like time and the standard deviation only like the square root of time. You should therefore expect Sharpe ratios for a year to be, I get it, the square root of 12 or 3.46 times as big as those for a month.
Jacob P: Right so this is a real problem when someone just comes along and tells you, our Sharpe ratios are blah and they don't tell you what time period they're talking about -
Tom Sosnoff: Right, well how are they going to know?
Tony Battista: Then it's all-
Jacob P: Because if they, right exactly like-
Tony Battista: You can pick a period can't you? Then it's all bull crap.
Tom Sosnoff: How's a sales person going to know?
Tony Battista: The salesperson has only given what's been shown to them.
Jacob P: The really have to like they can't, if someone does not tell you what time period the Sharpe ratio is computed for, then it only possibly means anything in comparison to other Sharpe ratios that they are simultaneously quoting you.
Tony Battista: It's like saying I made 8% this year but everybody else made 48%, I mean-
Tom Sosnoff: I'm going to tell you the way business gets done in America. The way money gets managed in big dollars in America. It is, it depends, who takes you to the super bowl and what golf course somebody take you in, because I promise you there's not a single person that allocates assets anywhere, that has ever asked the question, hey, because I sat through a million of these meetings-
Jacob P: Knowing what time period is this Sharpe ratio computed over.
Tom Sosnoff: Not only does nobody really know what the Sharpe ratio means, but they all have their own definitions of it. No one has ever asked the question, what time period or what's this measured against?
Jacob P: What was your benchmark? What was your time period?
Tom Sosnoff: Right what was your benchmark? They couldn't even name a benchmark. Let alone, you know, okay I get it now and I'm even more discouraged because now I realize how much bull shit has been, how many meetings I've sat through and they sit there and try to explain why one person's Sharpe ratio is better than the other one when it's all, when nobody's put any definition around it at all.
Jacob P: Listen I'm not coming in here to just tell you that things are not bullshit.
Tom Sosnoff: I'm saying this is so….
Tony Battista: If Tom is my benchmark then what's my Sharpe ratio?
Tom Sosnoff: Who'd my friend? That's what it is.
Jacob P: How do you perform in excess of Tom?
Tom Sosnoff: Oh god not even close. He's a minus 3.
Jacob P: Minus 3 alright.
Tom Sosnoff: What does this tell us?
Jacob P: Right, so okay, there is something to be gotten by looking at a Sharpe ratio. If you, sort of as an in house thing, if you are-
Tom Sosnoff: Oh in house I completely understand, because it's your numbers.
Jacob P: Right, if it's your numbers, if you're being consistent about your time frame, if you got, this is what your benchmark and you just really want to know how is this asset or this manager performing to compared to how is this asset or this manager performing and maybe you don't just care about their net gains, you also want to know how stable are their gains and then the Sharpe ratio is a very useful thing.
Tom Sosnoff: Absolutely. I have friends that manage either proprietary accounts of their own capital or just have one customer and in a sense that they're just a traders for one big bank, or brokerage firm, individual, whatever it is. Their Sharpe ratios have always made sense to me and I didn't know why, because they were always able to measure against themselves and they didn't care, they didn't have anything to prove measuring against someone else. So when they would explain their methodology to me, I'd be like this is interesting but I didn't know why it was interesting. Now I know why it's interesting.
Jacob P: Yeah. Alright.
Tom Sosnoff: Okay I got somewhere today. I like this.
Jacob P: Anyway so then this slide is really just saying why, sort of the obvious thing about why a higher Sharpe ratio is better and it's a high expected return, that's better if you have the same variability and if you have two things with the same positive effect return, well then you probably want the one with the lower standard deviation, because that'll get you the same good results more….
Tom Sosnoff: Does the lower standard deviation, in this case, mean less risk or does it mean that maybe that maybe whatever those assets are have just performed, had they been in a predictable range for X amount of time?
Jacob P: Really what it means is a higher correlation with the benchmark.
Tom Sosnoff: Higher correlation with the benchmark, so it's not really risk driven then?
Jacob P: It's not really risk driven unless you, unless risk-free rate is your benchmark, in which case it is.
Tom Sosnoff: Okay.
Jacob P: If you get something like S&P's you view that as inherent value of a dollar and you're wondering how this asset is going to fluctuate around there.
Tom Sosnoff: Will the magnitude of the change is not really apart of the equation?
Jacob P: Well the standard deviation has the magnitude of the change in it.

Tom Sosnoff: The standard deviation does? Okay, right.
Jacob P: In particular, like, if you're viewing something like maybe you think to yourself that you want one expected move to the downside to be like your amount of capital you want to risk.
Tom Sosnoff: Right.
Jacob P: In that case the Sharpe ratio is a really good way to compare two things because if something has a higher Sharpe ratio then you know that you can look at standard deviation. Figure out how much risk you want to put into it and that, that one will have the better expected return than something else -
Tom Sosnoff: So we just figured it out. Anyone who can explain the Sharpe ratio to me. I never want them trading for me.
Tony Battista: Is lying.
Tom Sosnoff: No no I just don't want them trading ever. Never ever want them trading for me because if you can explain the Sharpe ratio you can't trade. Other situations are more complicated but still a higher Sharpe ratio is a sign of a better investment. For example if one asset has twice the standard deviation and slightly more than twice the expected excess return of another, then it's Sharpe ratio will be higher. If we invest half as much into the riskier asset we will have the same exposure to an unfortunate move of expected size, but a larger expected return. That totally makes sense, but that kind of goes a little bit against, the view that we have of opportunity. One would argue opportunity is not a constant. I would argue opportunity is not a constant. Opportunity is cyclical, and if opportunity is cyclical then we found that you get more success when you scale into opportunity. Based on that thought process you would be, you would go the other way. In other words, you'd scale back because of the greater potential with, do you know what I'm saying?
Jacob P: Where you scale back, you'd scale back because of the greater potential for loss, if it was just the greater potential for gain of course you'd go into it. Right that would just-
Tom Sosnoff: Wherever there's a greater potential for gain there's a greater potential for loss. That model doesn't change so that's not the answer. I think what I'm saying is, what we found through all our studies in the last year and a half, last couple years. Has been that when opportunity presents itself because opportunity is cyclical and because extremes are cyclical, because as much as we want to think the markets are all random all the time, they're not. Let me change that, as much as we like-
Tony Battista: Because they are.
Tom Sosnoff: The randomness is not always predictable so what happens is you get these -
Tony Battista: Because there's an outlier that moves one way or the other first, there's a period of time last year being a bullshitter.
Tom Sosnoff: For all the reason. Markets always end up random, but they may not be random like today and tomorrow.
Tony Battista: For a shorter period.
Tom Sosnoff: So what we have then, but we're not trying to figure that out or predict that, but what we're saying is that opportunity then becomes maybe a little bit more cyclical. If opportunity is cyclical then you have to scale into opportunity we've actually done a lot of studies showing that when yous scale into the strength of opportunity. We've actually done a lot of studies showing that when scale into the strength of opportunity, which means scale like, scale into higher implied volatility scale into whatever it is. Then you actually do a lot better. It's like most people de-lever when the markets go down. If you lever when the markets go down you actually end up doing better.
Jacob P: Right, you generally have a contrarian opinion about a lot of things. You want to flip on the Sharpe ratio that's a very reasonable thing
Tom Sosnoff: Okay. I got it. I'm starting to understand.
Jacob P: It's possible that you look at the Sharpe ratio and go this isn't the reasonable statistic because I don't want that low standard deviation in the denominator. The Sharpe ratio- The low standard deviation of the denominator sort of saying you have a highly correlated asset and maybe you want your uncorrelated asset, you want these sort of highly volatile assets.
Tom Sosnoff: So how can, let me finish this and we'll go to the next one, but while it is good that the ratio is unitless, it can make Sharpe ratio hard to interpret. An investor who decided to pay attention to Sharpe ratios likely needs to spend some time getting a sense for how to judge their meaning. Just don't forget to adjust for the time period. You've said this a couple times.
Jacob P: Yeah it's like the biggest-
Tom Sosnoff: How is the layperson, like-
Jacob P: Takeaway here is probably the layperson is better off completely ignoring any Sharpe ratios, and sort of taking your tact of anytime anyone tells you a sharp ratio becoming a little bit distrustful.
Tom Sosnoff: Well because no one would tell you a Sharpe ratio that's not, you know-
Jacob P: That's not supposed to be good.
Tom Sosnoff: Right if you say to somebody, what's your return and you lost money and you're registered you have to tell them. If you say to some, but nobody says to them, what's your Sharpe ratio?
Jacob P: Right.
Tom Sosnoff: Okay.
Jacob P: Right no one ever asks for the Sharpe ratio so any time it's going to be handed out it's because it happened to be good that time.
Tom Sosnoff: So what doesn't this tell us? The primary problem with relying on the Sharpe ratio, once you get passed learning to have a feel for what .05 means, is that it relies on the standard deviation to completely characterize the variability of the returns. For normal distribution this is sufficient and most people uses of standard deviation essentially relies on treating all distribution as normal. Of course we, that's the limitations of what we have in front of us, technology wise.
Jacob P: You could also choose to look at these log normal graphs and these graphs with skews and kurtosis in them and get kind of a, I don't know, I personally get a pretty good feel when I look at a distribution graph for how it falls-
Tom Sosnoff: You're not normal.
Jacob P: I know.
Tom Sosnoff: Okay.
Jacob P: I really do think that one of the key risk here is that, standard deviation tends to understate risk in things that have kurtosis and fat tails and in most of the things we interact with in the market sort of have these fat tails.
Tom Sosnoff: How could it not? I mean you can't overstate the risk, all the other, the problem with, let me just, I got this logged off here, but the problem with overstating risk is, doesn't that just throw everything else off? You can't overstate risk. You can't overstate the fat tail risk because one it's an unknown and two it throws off everything else.
Jacob P: Well no, no, what I mean is that, when we use, when someone says the standard deviation then all of a sudden you think of a pretty good idea, like the whole concept of how much risk there is.
Tom Sosnoff: Isn't that the whole checks and balances thing. That's what keeps everything else in line, that's what creates all the opportunity for everything that we do.
Jacob P: Well the thing is you can create multiple distributions which have the exact same standard deviation, but with the one that has way more kurtosis is actually just way more risk.
Tom Sosnoff: Hold on a second. In reality skew and kurtosis show that many returns are not normally distributed and so the Sharpe ratio won't be capturing the actual risk involved. Even in the last example where we considered the standard deviation as the size of an expected move, in distribution with kurtosis, expected moves are actually larger than standard deviations.
Jacob P: So convexity says that expected move are always a little bit larger than standard deviations but for normal distributions they're pretty close, but for kurtosis distributions the can be much higher, the expected move can be much higher than a standard deviation.
Tom Sosnoff: How do you define a kurtosis distribution?
Jacob P: It's something which has a fourth moment in excess of the normal's distributions fourth moment.
Tony Battista: Either that or the Kurtosis is just bad breath, one of the two.
Jacob P: Kurtosis is like, is a fat tail like statement.
Tom Sosnoff: Okay.
Tony Battista: Kurtosis.
Tom Sosnoff: Kurtosis, it's the fourth definition.
Jacob P: Fourth moment.
Tom Sosnoff: Fourth moment.
Jacob P: The fourth moment.
Tom Sosnoff: Additionally-
Tony Battista: That's when you want to give someone the back of the hand.
Tom Sosnoff: What?
Tony Battista: That's when you want to give someone the back of the hand.
Tom Sosnoff: Don't you give me that kurtosis anymore. Don't you even start going down the road of kurtosis. That's when you know you're desperate and you're losing the argument and you pull out the word kurtosis. Yeah but you don't know anything about kurtosis!
Tony Battista: Of course not.
Tom Sosnoff: Additionally, it can be smart to be wary of good Sharpe ratios. Overly high Sharpe ratios are one of the red flags that investigators look for when searching for fraud. Remember if something seems too good to be true, it very well might be. Thank you Bernie Madoff.
Jacob P: Right if someone is consistently, very reliably, outperforming the benchmark without that much variation around that, that's really suspicious.
Tom Sosnoff: We've said that for a billion years, like you have to, the problem is you can't figure that out on your own. Until you're active. It's essentially activity that creates that type of understanding for sure.
Jacob P: It's also activity that can give you good Sharpe ratios without it being based on cheating or anything because a lot of activity can get your variability down, while keeping your returns kind of the same. This is the whole many occurrences, low correlation.
Tom Sosnoff: Of course. It's beautiful we're behind but that was-
Jacob P: Yeah sorry.
Tom Sosnoff: A great catch up and, no, no, no worries, and I don't think anybody will ever pine for the-
Tony Battista: Good job out of you Jacob, that's what he's trying, what he's trying to say and can't say because of kurtosis is good job out of you Jacob.
Jacob P: Alright, because of kurtosis.
Tony Battista: And we'll be back in 90 seconds we got a bootstrapper next, this is tastylive live.
Tom Sosnoff: That was really good.
Jacob P: Yeah. I know last week-