- Speaker #0
Hello, welcome back to Papers with Backtest podcast. Today we dive into another Algo trading research paper.
- Speaker #1
Indeed, and today we're tackling a 12-month cycle and cross-section of stocks returns. It's by Stephen Heston and Ronnie Sodka from back in 2004.
- Speaker #0
Okay, Heston and Sodka. So let's unpack this a bit. The main question they're asking is, does seasonality actually matter much for expected returns across different stocks?
- Speaker #1
Exactly. You know, you kind of think it should. Right. Some businesses are seasonal. We hear about the January effect for the whole market. Right.
- Speaker #0
Seems intuitive.
- Speaker #1
But the initial surprise in the paper is that if you use the standard ways of looking at it across the whole year, well, there's not much signed or predictable differences between stocks. Huh.
- Speaker #0
So year-round, looking across stocks, it's kind of flat. Not much predictability there. That feels a bit odd.
- Speaker #1
It does seem odd. But, and this is the key thing, they then went deeper. They looked at each calendar month on its own. Ah,
- Speaker #0
okay. Month by month.
- Speaker #1
Yes. And that's where they found it. Really substantial variation in expected returns. When you slice the data that way, it strongly points to a seasonal pattern that just gets, you know, washed out in the yearly average.
- Speaker #0
Gotcha. So the yearly average hides the action. Did they quantify this monthly swing at all?
- Speaker #1
They did, yeah. They estimated the annualized standard deviation of this seasonal part of expected returns at 13.8%.
- Speaker #0
13.8%. That sounds pretty significant, actually.
- Speaker #1
It is. It suggests the market might be much more predictable seasonally than people usually think. It really challenges the idea that expected returns are just constant month to month.
- Speaker #0
OK, so that's a big number to keep in mind. So our mission for this deep dive is really to get into the trading rules they came up with based on the seasonal effect and crucially how those rules actually performed in back tests.
- Speaker #1
Absolutely. Let's start with the strategies. First up are the weighted relative strength strategies or WRSS.
- Speaker #0
WRSS. OK, so you mentioned the year round view was flat. But they developed specific strategies. What's the idea behind WRSS?
- Speaker #1
Well, at its core, it's momentum. You know, buy stocks that did well historically, sell the ones that did poorly.
- Speaker #0
Standard momentum idea.
- Speaker #1
Right. And their first check, using various lookbacks across all months, didn't show much. Actually, a tiny negative return. Statistically, zero, basically. Minus 0.00009% per month.
- Speaker #0
So just standard momentum across all months. Nothing there.
- Speaker #1
Pretty much. But then came the seasonal twist. They specifically looked at returns at annual lags. So comparing this month to the same month, one year ago, two years ago, three years ago, and so on. Ah,
- Speaker #0
only looking back at the same calendar month.
- Speaker #1
Exactly. And then the strategy started showing positive returns. Now it looks small initially, just 1.33 basis points per month.
- Speaker #0
Wait, 1.33 basis points? It's like 0.0133%, right? Sounds tiny.
- Speaker #1
Why is that a big deal? It sounds tiny, but remember that previous number, that 1.33 basis points. consistently applied month after month based on this annual lag is what implies that big 13.8% annualized standard deviation in expected returns.
- Speaker #0
Ah, okay. So the small return points to a much larger underlying seasonal predictability. Got it.
- Speaker #1
Exactly. It's about the implication for the variance of expected returns. And they also found this effect wasn't the same every month.
- Speaker #0
Right. You said they looked month by month earlier.
- Speaker #1
Yeah. The variance the spread in expected returns was different depending on the calendar month. It was particularly high in January. Huge, actually, like 35.5% annualized standard deviation just for January.
- Speaker #0
Yeah, January's special again.
- Speaker #1
Seems so. But importantly, the effect was positive in all 12 months, just stronger in some than others.
- Speaker #0
Okay, so WRSS using annual lags shows promise. What other strategies did they test? You mentioned winner-loser deciles.
- Speaker #1
Yes, the winner-loser deciles spread strategies. Maybe a bit easier to grasp. Each month, You rank all the stocks based on their past performance over some period.
- Speaker #0
Okay, rank them.
- Speaker #1
Then you buy the top 10%, the winners, and you short the bottom 10%, the losers. Then see how that basket performs next month.
- Speaker #0
Makes sense. Long winners, short losers. Classic spread. How did that do with different look-back periods, the lags?
- Speaker #1
Okay, so if they rank based on the last 12 months, the one-year lag, the winner-loser spread, made about 1.46% per month. Pretty good.
- Speaker #0
Yeah, that's decent.
- Speaker #1
But what's really interesting is if they only use the return from exactly 12 months ago, just that single month's return, that strategy alone captured most of it, 1.15% per month, and it actually had a better Sharpe ratio.
- Speaker #0
So just knowing how a stock did in the same month last year was almost as good, maybe even better risk adjusted than looking at the whole year.
- Speaker #1
Seems like it. The signal from that specific month is really strong.
- Speaker #0
Okay. What about longer lags, like years ago?
- Speaker #1
Right. So they looked at lags of two to five years, but only using the annual months. So looking back, 24, 36, 48, and 60 months.
- Speaker #0
Just those specific months again.
- Speaker #1
Just those. And surprisingly, they found positive returns again, average 0.67% per month.
- Speaker #0
Okay. Why is that surprising?
- Speaker #1
Because if you looked at all the months over that same two to five year period, the return was negative, strongly negative, actually, like negative 1.07 percent per month.
- Speaker #0
Whoa, hang on. So looking at the same month two, three, four or five years ago gives a positive signal. But looking at all the months in between gives a negative signal.
- Speaker #1
Exactly. It's kind of wild, isn't it? It really emphasizes that the annual cycle is key. The intervening months seem to contain reverse information or at least noise.
- Speaker #0
That is fascinating. What about even longer lags? Did they go further back?
- Speaker #1
They did. And the pattern held. Looking at annual months only, from 6 to 10 years back, positive returns, 0.68% per month, statistically significant. Wow. 11 to 15 years back, same thing, 0.66% per month, significant. Even 16 to 20 years back, still positive, 0.52% per month, and significant.
- Speaker #0
20 years. That's... That's incredible persistence for a market anomaly.
- Speaker #1
It really is. And just to hammer the point home, when they looked at non-annual lags, 13 months or 18 months, anything not a multiple of 12. Yeah,
- Speaker #0
let me guess, negative.
- Speaker #1
Generally negative, yeah. And often significantly so. It really seems tied specifically to that 12-month cycle.
- Speaker #0
Okay, this annual thing seems really robust. Now, you mentioned they did some adjustments for average returns. Why bother with that?
- Speaker #1
Ah, good question. That's about figuring out why this works. always do well in January for instance and others always do poorly like a fixed effect right are we just picking up stocks that happen to have permanently higher low returns in certain months exactly so they tried removing the average return of each stock before ranking them first they tried removing the average calculated across all months and did that kill the strategy nope didn't really eliminate the profitability of the annual strategies much at all okay but then the crucial step They adjusted by seasonal average returns. So for each stock in January, they subtracted its average January return from previous years. For February, its average February return, and so on. Ah,
- Speaker #0
taking out the stock's typical performance just for that specific calendar month.
- Speaker #1
Precisely. And that adjustment significantly knocked down the one-year annual effect. And for the longer-term annual strategies, it made the profits statistically insignificant. Uh-huh.
- Speaker #0
So that really nails it down. The profit isn't just from stocks being generally good or bad. It's from them deviating from their own typical seasonal pattern for that month. It's driven by seasonal shifts and expected returns.
- Speaker #1
That's the strong implication. Yes. It really isolates the seasonal dynamic.
- Speaker #0
Okay. That makes sense. Did they show which months these annual strategies worked best in? You mentioned January earlier for the variants.
- Speaker #1
Yeah. They broke down the profits by calendar month. And yes, January stood out for high returns for the annual strategies, but also October and November were notably strong.
- Speaker #0
Any examples?
- Speaker #1
Well, that two to five year annual strategy we talked about, it averaged a whopping 3.89% just in January. That's 4%. In one month. Yeah. And it was over 1% in November and December too. It shows how powerful these effects can be in certain parts of the year.
- Speaker #0
Definitely highlights the potential. Now, any good study needs robustness checks. Did this hold up across different types of companies, like big or small?
- Speaker #1
Good point. They checked size. Interestingly, the annual strategies, especially the longer term ones like 2, 5 and 6, 10 years, were often more pronounced in large firms.
- Speaker #0
Oh, really? Not just a small cap effect then. That's often where you find these anomalies.
- Speaker #1
Right. This seems present, maybe even stronger in bigger stocks too.
- Speaker #0
What about industry? Could it just be, you know, tech does well in Q4, retail in Q1, that kind of thing?
- Speaker #1
They looked at that too. It seems the effect is happening mostly within industries.
- Speaker #0
Within. So. Comparing tech stock A to tech stock B based on their same month performance last year.
- Speaker #1
Exactly. When they calculated the returns relative to industry peers, the results were still significant. Very similar to the raw returns. So it's not just about whole sectors moving together seasonally.
- Speaker #0
That's quite specific then. Okay, one more potential explanation. Earnings announcements. They often happen around the same time each year, right? Could this just be related to earnings news?
- Speaker #1
They checked that. They confirmed prior work. showing that short-term, non-annual momentum is clustered around earnings dates. No surprise there. But the longer horizon annual strategies, they showed similar profitability whether it was an earnings announcement month or not.
- Speaker #0
Ah, so the seasonal effect seems distinct from the earnings announcement cycle.
- Speaker #1
That's what the evidence suggests. It's not just picking up predictable earnings news.
- Speaker #0
So it's robust to size, happens within industries, and isn't just earnings. Did they offer any solid explanations then?
- Speaker #1
They touched on possibilities. Standard risk factors, size, value, beta, the usual suspects didn't seem to explain it.
- Speaker #0
Okay, not standard risk.
- Speaker #1
They did notice similar seasonal patterns in trading volume, which hints maybe at a link to liquidity, but it's more of an observation. Hmm,
- Speaker #0
liquidity. Plausible, maybe.
- Speaker #1
And they did caution about transaction costs. These strategies, especially rebalancing every month based on annual lags, could involve more trading than simple buy and hold or even standard momentum. And costs might be higher in, say, January when the effect is strongest.
- Speaker #0
Paper profits are one thing, real-world implementation with costs is another. Always the catch.
- Speaker #1
Always. So while the paper convincingly shows these patterns exist and seem exploitable, the why is still a bit fuzzy. Needs more research.
- Speaker #0
Okay, so summing this up. This Heston and Sodka paper really shows there are significant, persistent seasonal patterns in stock returns. But you have to look specifically at annual intervals, same month, different year.
- Speaker #1
Exactly. And trading strategies built on that specific idea, buying last year's winners for that month, selling the losers, showed pretty remarkable profitability in their backtests.
- Speaker #0
And importantly, this seems driven by actual seasonal changes in expected returns, not just risks or earnings.
- Speaker #1
That's the key takeaway. It's quite surprising, really, that just focusing on the calendar month reveals this predictability that gets completely missed otherwise.
- Speaker #0
It really makes you think, doesn't it? Maybe our standard asset pricing models are missing a piece of the puzzle by ignoring the seasonal structure.
- Speaker #1
It's just that. How do we best model these recurring patterns? That's a big question this paper leaves us with.
- Speaker #0
Definitely food for thought. Well, this has been a really interesting deep dive into the power of the calendar in stock returns.
- Speaker #1
It certainly has. A fascinating paper.
- Speaker #0
Thank you for tuning in to Papers with Backtest podcast. We hope today's episode gave you useful insights. Join us next time as we break down more research. And for more papers and backtests, find us at https.paperswithbacktest.com. Happy trading.
