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I intend to (and already did) copy Jim a little who once said his CAGR with BRK since around 2000 is 24.x% (that's how I remember it: probably not too far off) by using leverage: Buying calls when PeakPB/Price is low, puts when it's high, based on his observation that the typical range is 1.2-1.55 (just once in 20 years much lower than 1.2).

As 1.2/1.55 is rare: Surely Jim did analyze that in depth and has numbers for the different intervals, kind of 'Since 2000 3% of the time it traded at 1.2-1.3, 5% at 1.3-1.5' or similar. Generous as he is Jim probably once posted such numbers. As after his 83 days holiday he should not be immediatedly overwhelmed with requests: Does anybody has his numbers (link to his old post or the numbers themselves)?

Here's a fresh table.

Average one year forward REAL returns, based on ratio of price to peak-to-date book per share on purchase date.
Ending dates smoothed a bit.

First column is the average price-to-peak-book in that bucket. Each bucket is 1/20th of the observation start dates.
Second column is the average real one year return starting with a P/peakB in that bucket.
Third column is my smoothing of that data.
(I did a linear fit, and a cubic fit, and averaged those two results)

P/Peak    Obser     Model
1.075     34.6%     30.1%
1.165     22.2%     20.6%
1.204     19.1%     17.5%
1.250     15.4%     14.5%
1.295     10.5%     12.1%
1.323      4.6%     10.8%
1.343      5.5%     10.0%
1.359      9.7%      9.4%
1.376      8.5%      8.8%
1.392      5.5%      8.2%
1.412      4.5%      7.6%
1.438      5.7%      6.9%
1.461      6.8%      6.2%
1.483      5.3%      5.6%
1.509      7.7%      4.9%
1.537      8.1%      4.0%
1.579      3.5%      2.7%
1.638      4.0%      0.4%
1.693     -2.2%     -2.4%
1.808    -12.0%    -10.9%

1.303               11.7%  today

Last row is today with price at precisely $300 / $450000.
So, if the next year resembles the average stretch in the last ~20 years, one would expect a one year return of inflation + 11.7% in the next year.
That will be wrong, of course, but the idea is that it's a 50/50 shot whether it's too high or too low.

BUT...
You should probably knock about 4% off that expectation because the P/B multiples were so much higher 2003-2007 than in recent years.
If I look only at my sundry models starting with data from 2008, the implied expectations are more like inflation + 7.7%. Still not bad.
The rate of growth in value per share has been remarkably constant...it's the market multiples that make the difference.

Jim

The rate of growth in value per share has been remarkably constant...it's the market multiples that make the difference.

...and the fact that some of my models use valuation metric inputs that have slipped a bit lately, which price-to-peak-book can't do.

Jim

Jim, thank you!

Do you have data how long Price/PeakBV per share was in each bucket, in each of those 19 intervals (% of the total observation period)? This question is superfluous and already answered IF your for me a bit mysterious

Each bucket is 1/20th of the observation start dates.

means this:
...... 'Price/PeakBV was the same length of time in each interval'
or in other words:
...... 'Each interval represents 1/20th of the days of the total observation period'
Which I suspect it does mean, as the width of the intervals resemble a bell curve, as expected in this case more narrow towards the middle Price/PeakBV)?

P.S.: Sorry if this is not understandable. I am having problems with my English here, don't know how better to express what I mean.

Do you have data how long Price/PeakBV per share was in each bucket

No, the widths of the buckets aren't bell curve shaped...
It isn't divided into equal intervals of P/peakB, but equal by number of days.
(that's why the P/B values near the middle of hte table are so close together: there were lots of days near those values)

Each bucket was 1/20th of the purchase dates since the start of January 2003.
Since the return observations were a year forward, the last start date was about a year ago.
So, the start date range was 2003-01-02 through 2021-11-16, which is 18.87 years of start dates.
Divide by 20, and each bucket is the average return across 0.94 years (11.3 months) of start dates with similar starting price-to-peak-book values.

The individual purchase dates aren't independent observations, of course.

Jim

the widths of the buckets...
divided...equal by number of days.

Great! That's what I meant (plotting P/B on X axis and number of days on Y is bell shaped (extreme P/B is rare), therefore dividing that curve into intervals with an equal number of days becomes more narrow towards the middle).

Clarified - and very helpful in developing a leverage strategy!

Clarified - and very helpful in developing a leverage strategy!

Looking back at your initial post - it sounds like you're following the same path of interest I took a couple years ago, inspired by Jim's findings.

In that case, I highly recommend running a backtest of the approach you have in mind as I did (e.g., applying leverage at whichever cut-offs you have in mind and removing it at others).

I've found in the past that translating bucket of return type of data like this into a trading strategy with cut-offs does not always produce the slam dunk results one might intuitively assume.

I found that to be true in this case. When I backtested a few years ago, the best I recall seeing was a ~1% CAGR advantage, but it also seemed quite fragile (e.g., adjusting the thresholds up or down a bit wiped that advantage out).

I can't confidently say I know why that strategy produced such a small advantage given the incredibly smooth fall/rise in the P/B bucket forward returns in the table, but I suspect it's related to the data in the buckets not being independent observations as Jim said.

However, if you (or Jim) have found otherwise from your testing (i.e., a mechanical strategy that produced a larger advantage), I'd love to hear it! I'd be thrilled to learn that I made a mistake or that there's some nuance I missed.

Knighted, seems you know exactly what I intend. I am inspired by 2x this year having bought BRK calls when Price/PeakBV was in one of the lowest of Jim's buckets. First Jan'24 calls which until 3 days ago were up around 40%, then Sep29 (Price/PeakBV=1.22) Jan'25 calls which were up over 70%. That ignited the thought to extend that strategy to not act on only the extremes but going a bit up the 'bucket ladder' => buying calls already at higher Price/PeakBV than around 1.2x to have more such actionable events. That's why I asked Jim for those data. When you are now saying

I've found in the past that translating bucket of return type of data like this into a trading strategy with cut-offs does not always produce the slam dunk results one might intuitively assume. I found that to be true in this case. When I backtested a few years ago, the best I recall seeing was a ~1% CAGR advantage

the question for me is: Did you find this to apply also to staying with valuation extremes like 1.3x (or lower), or only when you go far higher, much more into the middle of the valuation range?

I intend to (and already did) copy Jim a little who once said his CAGR with BRK since around 2000 is 24.x% (that's how I remember it: probably not too far off) by using leverage: Buying calls when PeakPB/Price is low, puts when it's high, based on his observation that the typical range is 1.2-1.55 (just once in 20 years much lower than 1.2).

I've done very well buying and selling options on Berkshire, not as well as Jim but still very well. One thing I worry about with an options strategy is what happens when Buffett leaves the building for the last time. I think it's possible that the stock price (not IV!) stays subdued for an extended period of time which might make options less attractive for a couple of years, especially with a higher implied interest rate. So far I haven't changed my strategy at all but I'm thinking about being somewhat less agressive to be able to roll calls multiple times.

the question for me is: Did you find this to apply also to staying with valuation extremes like 1.3x (or lower), or only when you go far higher, much more into the middle of the valuation range?

Good question - I can't recall! Too much time has passed since I took a look at this. I hunted for the data/assumptions I used back then but failed to find it (another lesson learned for being more organized). So I was inspired to re-do the analysis using the 2x leverage example you mentioned and this time did a comprehensive analysis consisting of all permutations.

I've uploaded a heat map chart that summarizes the results showing CAGR for different thresholds:

https://ibb.co/P9QQ4NL

To read it, find the P/B value on the x-axis you would want to start applying 2x leverage at/below, and then trace it up to the y-axis value where you'd want to sell and go to cash at, re-buying (at long, 1x) once it dips below that value again. That's the CAGR the strategy would have yielded (not accounting for trading costs).

The pink entries at/below ~9% represent BRK's CAGR for buy and hold over this time period for comparison. Anything at/below these values are worse than B&H.

The results are quite a bit more favorable than I remembered from previously. I think this is because I assumed a smaller amount of leverage, 1.3x or 1.4x I think, since I was looking at using very DITM calls and was more risk averse. I think I also tried to take into account trading cost estimates, and I was looking at thresholds of leverage at P/B <=1.2 and going to cash at levels >=1.5 which maybe weren't the optimal cherry picked ones.

Keep in mind, while some of these numbers look very high, as you move further to the right on the x-axis, you're also spending a lot greater % of time invested at 2x leverage which adds additional risk.

Highly interesting table, thank you!

From my interpretation I feel confirmed in my intention to buy the longest LEAP's when Price/PeakBV is in the 1.2x range and to sell when it's again with around 1.4x at a middle valuation. Those on Peak(!)BV based numbers are not directly comparable but a very wild approximation might be to look in your table at 'Buying at 1.3x, selling at 1.5x', resulting in 17% CAGR, an incredible 8% improvement to buy and hold.

Doing such with the pure strategy of your backtest and therefore 100% of one's Berkshire holdings would be an incredible risk (wiped out by one super-long bad stretch), but doing such with 'Play/Casino' money seems to be worthwhile.

Please correct me if my thinking or interpretation of your table is flawed or you just see it differently.

I highly recommend running a backtest of the approach you have in mind as I did
I would like to do that, as I just found that my idea to base buy/sell actions solely on Price/PeakBV as in

- Buy calls when Price/PeakBV falls to 1.2 in Jim's table
- Sell at 1.4

is too simple --- no matter what thresholds used! The problem is the selling. That became clear by looking at EVBigMacMeal's Price/BV table, together with a 20 year chart. A good example is the stretch 2008-2014. To simplify let's use just Price/BV (instead of Peak).

- 2008 and 2009 Price/BV fell drastic, from 1,81 to 1,17 => somewhere in 2009 such a strategy would have bought calls, with the BRK/A share price then around $100,000.
- It would have taken a full 5 years until the sell threshold of 1.4 was reached again => the calls expired worthless or with the same effect would have been rolled out numerous times.

But while Price/BV stayed depressed for many years BV and share price did not. Already in 2009 the share price moved constantly upward from it's low and apart from 2011 continued to do so for all those years.

So buying when Price/BV = 1.2 would have enabled one to sell those shares bought in 2009 for $100,000 at nearly ANY point in time during the following 5 years of still depressed Price/BV very profitable: +20% end 2010, +15% end 2011, +78% end 2012 etc.

My conclusion:
- For shares it's simple: When Price/BV is really low put every cent you don't need for a while into Berkshire.
- For calls: The decision to sell has to be a function rather of Price appreciation than Price/BV!

It's probably not necessary to develop a mechanistic formula. But if so a 'sell formula' should weight Price appreciation FAR highest, followed by Price/BV and Time (which because of the price decay of options plays a role too in the sell decision).

I hope this thread continues. I am very curious what you, knighted, and other knowledgeable posters here think of that.


P.S.: EVBigMacMeal's tables provide one BV data point per year. To do a real backtest continuous BV and price data are required. Does anybody has a link to a FREE souce?

- Buy calls when Price/PeakBV falls to 1.2 in Jim's table
- Sell at 1.4...

Though there are many such schemes possible, I think the main lesson is just that it makes sense to hold more when it's cheap and less when it's expensive.
When it's cheap you know that the near future (time frame unknown, but rarely more than a year or two) will offer you a one time return in excess of the long term trend rate of value growth.
When it's expensive, you know that the near future (time frame even more unknown) will contain a flat spot during which you will NOT get the long run trend rate of return.

So, what to do?
A backtest won't tell you the likelihood of seeing any given level of cheapness again in future.
But, if it does happen...react to it.
You'll know it when you see it.

Jim

A backtest won't tell you the likelihood of seeing any given level of cheapness again in future.
But your table does 😉:

It would have taken a full 5 years until the sell threshold of 1.4 was reached again => the calls expired worthless or with the same effect would have been rolled out numerous times.

This is what I struggle with.

In a worst case scenario where BRK remained low for an extended period of time, even DITM calls may expire worthless, and then you'd need to raise some money to buy new calls to keep the strategy going. The possibility of this happening multiple times is where the risk of kaboom (permanent loss of a lot of money) seems to exist.

Granted, it'd probably be a small risk, but we've had one Great Depression before, so we could certainly have another (or worse).

The challenge I wrestle with: I have no way to raise significantly more funds in most of my accounts if repeated worst case scenarios unfold.

I can't raise additional funds at all in my IRAs, so to mitigate this risk, I'd need to start out with a fraction of my funds committed to calls in those accounts (let's say 30%) and then only increase that if calls start expiring. And if we're talking DITM calls, the leverage is already pretty modest there (let's say 1.4x). So take that modest leverage and dilute it even further by 30% of funds, and then deduct trading costs, and I'm left mulling over whether it's even worth doing for the small advantage it might afford.

Taxable accounts on the other hand seem like a more lucrative place to try this with a larger % of the portfolio, but I don't have much equity in other assets (like my home) to tap if I needed to raise funds there. If I knew I could raise significant funds easily if the worst case above happened, that'd change things. I'm definitely a bit envious of Jim's previously stated ability to raise significant funds in this scenario!

On that note, if anyone has come up with creative ideas for a person without significant home equity or alternate assets to raise significant funds, I'd love to hear it!

As you are saying you have funds committed to calls: Isn't your 'Kaboom' scenario typical for options (T... calls for me were what the textile mill was for Warren = a painful lesson one should not forget)?

Forget my 'It would have taken a full 5 years until the sell threshold of 1.4 was reached again'. As said before, after looking at BRK charts + EVBigMacMeal's Price/BV table I am convinced this is the wrong approach anyway, that you use Price/BV for the decision to buy but not for selling. That decision has to depend mainly on price appreciation --- which would have worked every time during the last 20 years with 2-3 year long LEAP's, even during that 5 year stretch of depressed Price/BV. While that ratio stayed low BV and Price went up. One would have bought 2009 and already sold in 2010 --- and bought again in 2011 and sold again in 2012.

The critical question seems to be what price appreciation threshold to use for selling the calls. 10% share(!) price appreciation might strike a good balance between greed and making as sure as possible the threshold will be reached before the calls lose too much value or expire. That price appreciation for me would make it worthwhile as we might have different approachs to options: I would not raise additional funds to 'keep the strategy going', but limit my options exposure to 'money for playing in a casino'. The intention is to use with that play money supposedly unique opportunities of Berkshire undervaluation --- but then 'properly': Not with 1.4x leverage but rather as with the DOTM Jan'25 calls I bought end of Sep which had 3.7x leverage. And then 10% share price appreciation in a relatively short while translate into a very different percentage.

Yeah I just got on shrewd'm so I'm replying to old threads. You don't have to read these if you don't want to.

First off, it has been said before, and often by people who have tried it, but options strategies are HARD to use to make ADDITIONAL money. You PAY for leverage and the people you are paying think they are making money, so you should wonder what the implications are for whether you are making money or not. A good friend of mine made buckets of money for years. For years he

1) Mostly was just very long APPLE
2) Would trade around the edges selling puts to goose his returns.

He would analyze his results once in a while, comparing his long+options strategy to a "box of rocks" strategy of just staying long AAPL. What he found usually is he would have been better off just staying long AAPL stock. The box of rocks was smarter than the box of brains, at least if making money is your measure of IQ.

Later he traded a more volatile rising stock, and I did a relatively incomplete analysis of some of his options around the edges trading, and concluded that goosing your returns by selling puts was like going to Las Vegas, an expensive hobby that (it turns out mostly) he could afford because the underlying position was doing well.

***

Second off, and really more interesting, the data Mungofitch posted looks fun if plotted. I would characterize it as:

1) For Price/PeakBook < 1.35, the Price/PeakBook WANTS to be about 1.42 or so, and will get to a price that would have been 1.42 ratio in a year about 50% of the time.

2) For 1.35 < Price/PeakBook <= 1.64, P/PB wants to be 0.06 higher, and will get there within a year about 50% of the time.

3) P/PB does NOT want to be higher than 1.64 and price will drop to enforce this MORE than 50% of the time within a year.

Note that in the broad middle, P/PB wanting to be .06 higher does not mean you will make inflation + 6% on your stock. You are starting at 1.35 to 1.64 so a 0.06 rise gives price appreciation results of 0.06/1.35 down to 0.06/1.64 or 4.4% down to 3.7% real appreciation in a year.

****

It is a pleasure to be back on the old boards. Which by the way are much nicer now than they used to be, if that makes any sense :)

R:)

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