racemize

Well, it is to approximate the behavior of the set of rules. So, basically, I'm trying to assume that his rules always work perfectly and then determine if it makes sense to follow them, versus say just using the initial hurdle rate (his is 2-3x in 2-3 years). So far, I haven't been able to make a test that shows it is rational to hold cash according to his rules unless the event happens frequently enough and/or the returns are a multiple corresponding to the frequency of the event. Looking back over market returns, I do not think that happens. In reality, neither 1 nor 2 happen, but this is just to test whether the rules are rational. In a "real world" experiment, I would assume it would be even more in favor of not holding cash, since the returns are unpredictable, and probably less than 7x in 2-3 years. Please point out any issues though, or any other way to model returns/strategies where holding cash makes sense. I'm happy to try to generate the numbers to see if it works, as this is a question that I'm trying to answer for my own investments.

Gio, I knew you'd be on this thread! Responses below: Do you have some references for this that I could read? e.g., something outlining his strategy? I'd like to compare it against being fully invested, if possible. So far, I haven't found any model that indicates holding cash increases performance, unless you are a timing genius. To be clear, I started out thinking 5-10% cash was probably a good idea, but couldn't make the numbers work out in any realistic scenarios. Well certainly, but that's true for everything in the portfolio. My point is, if you have a process that works at a certain rate, and know that you have such opportunities around, it appears that it is best to invest and not hold cash for some other reason (e.g., demanding a higher hurdle for the last bit of cash). Actually, this is exactly my point. If they aren't predictable, then holding cash is an opportunity cost that goes up almost all the time. Unless holding that cash pays off for the events when they happen, it is not worth doing. I have not found any evidence/model that allows the cash to overcome this opportunity cost. In fact, if there is a time or rule set where you can tell me it is good to hold 5% cash, then it will also say you should have held 100%. Either holding cash helps or it hurts over the long term--I haven't found any evidence that it helps long-term performance. Please let me know if there is any evidence! I'm looking for it. AL2012 If we are not to learn from those great and very successful minds of the past, how are we supposed to navigate the perilous waters of investing? Well, this is with regard to a business--a business should have cash reserves, but that is besides the point. I'm referring to the portion of money that is designated for investments, so that would be outside of cash reserves for persons or for businesses. For that investable money, the question is whether to hold cash, so I do not think the above quote applies. Moreover, I believe that someone asked Buffett how he would be invested if he had a smaller amount of capital in 1999, and he said 100% stocks. That's a hard thing to search for, but I'm pretty confident on the quote. I might be able to find it. Absolutely, and in those times cash should be raised!

Well, what I'm saying is it hurts all performance (not just short term). I'd rather handle the volatility than have lower long-term gains.

That's his reasoning, but all the models I've set up show long-term underperformance for holding the cash. Or, in other words, because the cash is held in order to take advantage of the rare higher opportunities, you end up with lower performance. The only way it works out is if the rare opportunities either 1: happen relatively frequently or 2: have enough upside to offset the lack of performance of the cash. e.g., if the event only happens every 5 years, the new investment has to be 5x greater than the normal rate of return. This hurdle seems extremely hard to overcome. If it is to simply reduce volatility, then I'd rather it be stated in an intellectually honest way, e.g., indicating that it sacrifices long term performance for lower volatility.

Hi All, I've been giving Pabrai's cash allocation model some thought for a while, and I'd like to get thoughts from the forum members, both on Pabrai's method and holding cash in general. First, I assume that everyone has some minimum hurdle rate for an investment, e.g., 10, 15, 20%, whatever. I assume that if an investment does not match the hurdle, it won't be made, so there are times that cash will occur simply because an investment cannot be found. This is not the situation I'm trying to focus on. Instead, what I'm trying to consider is whether or not cash should be held at times even though an investment opportunity exists that exceeds the hurdle rate. For example, after 2008, Pabrai has indicated that he thinks about cash allocation in the following manner: 1st 75% cash - 2x in 2-3 years next 10% cash - 3x in 2-3 years next 5% cash - 4x in 2-3 years next 5% cash - 5x in 2-3 years last 5% cash - >5x in 2-3 years Initially, I thought this was very rational and a good way to proceed. However, I wanted to model this type of behavior in a spreadsheet to see how high the opportunity cost is. For example, I initially modeled S&P returns and assumed an investor would invest fully only after big down turns (e.g., 2003, 2008), which happen every 5 years or so. The results were under-performance for all cash levels. Then, I modeled 15% returns with cash allocation where the cash would be used every 5 years for extraordinary returns. The results were essentially that you had to put the cash into something that was 5x better than your "normal" rate of return (which makes sense, since the event happens every 5 years, in that model). Thus, after looking at these models, I'm drawn to the conclusion that keeping cash when you still have opportunities exceeding your hurdle rate is simply not a good idea. I think there are many who disagree with this. I would like to hear any thoughts people have on this idea in general; particularly if you disagree. If you do disagree, could you also indicate the assumptions you are making, so that it might be shown in a simple model? Thanks!

some nicer clothes. mine are getting old and I hate spending money or shopping.

I was looking around for information on how prices actually move for dividends. Found this paper, which indicated something like 80% of dividend amount. http://www.minneapolisfed.org/research/sr/sr173.pdf

yes, that's my only current thought as well. I'll have to do a lot of verifications to confirm it. The WFC example I just gave will be a starting point I think.

Apparently, I gave myself too good a price. Let me retry: Let's say we are one year from expiry: WFC = 60 WFC-WT = 35 strike = 30 warrants per share = 1.1 dividend thresh = 0.34 current div = .45

Yes, but I'm not asking about today. I'm asking how do I calculate the cost of leverage in 2016, at that point?

Ok, so hypothetical: It is 2016 and WFC has paid enough dividends to get shares per warrant to 1.1. Let's say current numbers are: Stock price: 60 current div: 0.45 per quarter div threshold: 0.34 shares per warrant: 1.1 warrant strike: adjusted down to $30 from 34.01 warrant cost: $32 Are you saying I can ignore the fact that it is 1.1 shares per warrant to calculate the new cost of leverage?

You just agreed (above) that it doesn't matter to the banker what you invest the money in that you borrowed. You only owe him interest on the money borrowed. I believe that adjustments after the fact will affect the economics of the amount you are borrowing, if you are looking at purchasing after the adjustments (not before). e.g., if I change the shares per warrant from 1 to 1.2, then the total returns change. Thus, ignoring that modification from 1->1.2 does not give accurate results, I believe. Or said another way, the intersection point has to change if I can buy 1.2 shares instead of 1 shares.

It would be the same as with the GM formula. You just treat 34 cents as the missed dividend cost expressed as a percentage of the strike price. You'll get a more accurate leverage cost estimate as compared to GM. After all, GM won't keep a dividend at 1.20 for each year -- they would raise it a bit each year. But WFC's lost dividend cost is capped at 34 cents -- so it doesn't have the complexity of the GM case. Yes, but what I'm trying to adjust for, is in say 3-4 years when the shares per warrant has changed for WFC (e.g., from 1 -> 1.1). At that point, I can't ignore that the shares per warrant is different and have to adjust for it when calculating the cost of leverage. Thus, while it isn't terribly useful now, it is something that will have to be taken into account when the shares per warrant starts changing (already has for a few of these). It is a minor difference at the 1.1 level, but a big one at the reverse split level. Current thought is to just normalize the numbers to 1 when I do the calculation itself, but that is rather inelegant.

Oh, I agree with all that, I'm just trying to account for the lost 0.01 per quarter for BAC. While it isn't as big a deal there, it is for say, WFC, who's threshold is $0.34 a quarter. I'll keep messing around with it until I have an adjustment I'm happy with.

Yeah, I was considering just undoing the splits. I wonder if that will still work for the cases where the shares per warrant is getting adjusted independently as well (e.g., where I'm calculating the missed 0.01 dividend for BAC, but ignoring everything above it since the warrant adjustments take care of it. Then you end up with strike price adjustments as well as additional shares per warrant). Actually, I should just be able to compare it against my old formula as long as the expiry is one year away, for verification. Feels very hacky though.

Well, I'm trying to deal with the case where you don't have adjustments up to a threshold, so in those cases you do (i.e., where the shares per warrant are changing due to other adjustments being made, not within our own formula for catching the dividends that weren't accounted for). We can ignore that more complicated case for now and just try to focus on this (which will solve the other case at the same time, I believe): Let's consider the citi case with a 10:1 reverse split: Before split: Warrant price = .63 Strike Price = 10.61 Common Price 5.08 Shares Per Warrant = 1 After Split: Warrant Price = .63 Strike Price = 106.1 Common Price = 50.8 Shares Per Warrant = 0.1 The formula needs to be able to deal with that--I know how to adjust it on my formula, since I know which parts the "shares per warrant" affects. I'm having a bit more trouble with this new formula, however.

Actually, I got a slightly different result (compared to txlaw) from my modified formula. They were very close, but a little bit different. I wonder if it's due to this effect: 1) The common stock owner would be reinvesting the dividend into extra shares. Therefore the dividend needs to be multiplied by the FULL amount of shares. The total share count grows each year when the dividends are reinvested. 2) My computation that compounds the warrant strike by 6.5% takes this into account (I think). It grows the dividend effectively as if it were reinvested into additional shares, each paying 6.5% worth of missed dividend cost. Each year, the dividend cost is 6.5% bigger than the prior year because there are more shares. Do you agree that makes sense? If you ignore the effect of the missed dividend growing each year (due to the increasing share count of reinvested dividends), then the computation comes out wrong. So I think if you want best accuracy you can't simply add 6.5% to .69%. It's relatively close though, but for the sake of exactness it misses by a bit. so this is still my best stab at it: 17.65*1.x^5.5=18.33*1.065^5.5 EDIT: Well, it's better than nothing because it does at least recognize that the share count is rising after each dividend. However, it might not be adjusting the share count properly because it would depend on how many shares are purchased with the dividend. A higher stock price would result in fewer added shares, and a lower stock price would result in greater added shares. This is why the BAC "A" warrant dividend protection formula takes into account stock price when it adjusts the warrants for paid dividends. So, now how do you adjust the formula when you can get more than one share per warrant? weeeeee.....

This was focusing on calls with no protection. For those with a threshold, we only have to worry about dividends below the threshold, as the others are accounted for.

I guess if we only had one year, then it would be the same right? Since there is no compounding? Assume: $10 stock $8 strike $3 cost of option $1 dividend 1 year expiry so extra payment is $1, which we subtract from the strike of $8 7*1.x=8*1.125 (which is the same as 8+1) = 28% cost of leverage My method also returns that. I think I just made it a tautological statement though...

How can we verify that this number is correct? Previously, we could look at returns of each vehicle, but with this formula, I'm unsure how we would compare the common to warrant. For example, the math I used before to test would show that the calculated price was too high with these new costs of leverage.

I believe it solves the problem where the dividends from the common are immediately reinvested into the common stock. I guess so, but you have to know the common price at those points to get an actual number, right?

I think it makes sense. The problem I have with these types of answers is that I don't see a good way to verify the result. How can we be sure that is the cost of leverage versus the common for example? Do we assume the dividends are reinvested? If so, at what rate do they compound? Or if we were reinvesting, we have to make assumptions about what prices we reinvest at. I guess it is inherently an approximation at this point.

yeah, I think I'm at the point where it is close enough, unless there are major problems with my current solution.

I guess I could calculate what the total returns would be if we reinvested dividends and see if it ended up being txlaw's result. That could take a while though...

That being said, I'm not sure that txlaw's method incorporates the missed compounding of dividends either--it seemed like it was just adding the missed yield relative to the strike to the premium cost of leverage portion. I suspect his method is too high and ours is too low. I'm not sure how to overcome this issue. Perhaps call it close enough, and know that it falls a little short.