Mohnish Pabrai Boston College Presentation

[racemize]

The background on how I came up with that equation...

 

1)  I don't know how to use Excel, so I wasn't going to go there

2)  I didn't want to have to plot two lines on a graph and find the point of intersection

 

So I just reasoned that the option premium is a cost that would have to be overcome in order to do just as well as the common.

 

So you subtract the option premium from the strike price to get a number.  Then you just have to ask at what rate that number needs to compound to get back to the strike price.  That rate will be the precise, exact breakeven point versus the regular common stock.

 

Were it to come up short, you would have not met the option premium hurdle -- so it would certainly have underperformed the common.  Were it to come up in excess of the options premium, then you would for certain have outperformed the common stock as you've exceeded the amount paid for the premium.

 

Make sense?

 

I'm not sure if it's in any text books or if it's used elsewhere -- probably, but I just came to this on my own out of avoidance of Excel.

 

So the option premium results in a "hole" in the value versus the common if the stock never appreciates before expiry -- the only way to break even versus the common is to precisely fill in that hole.

 

I believe that's exactly what I'm doing--finding the stock price at which the two vehicles have the same returns, which is the intersection point.

 

It makes a lot of sense to me.  The only way I know to calculate it with the dividends included is via the math I posted above.  I use a spreadsheet for it, as I calculate for a lot of warrants/options at the same time.

[ERICOPOLY]

Okay, I'm done with my thinking on this now (I know, famous last words).

 

Let's say you own a $10 call option and miss a $1 dividend.  The value of your call option drops by $1.

 

Now it's worth $9.  It has to compound by 11.11% in order to get back to $10 value.

 

So the cost of leverage (from this dividend alone) is actually 11.11%, not 10%.

 

GM stock at todays close:  $40.16

GM "B" warrant price:  $22.41

GM "B" warrant strike:  $18.33

 

Let Y = sum total of expected future dividends over the option period.

Let X = cost of leverage rate

 

$40.16 - $22.41 = $17.75

 

($17.75 - Y)*1.x^5 = $18.33

 

I used time period of 5 years for simplicity, even though it's not exactly 5 years to expiry.

 

 

Does this formula make sense to you guys?  I introduced "Y" to account for the lost dividends.

[ERICOPOLY]

Or it could be this:

 

$17.75*1.x^5 = Y+$18.33

 

What's your opinion?

 

I did have a large beer at lunch which is making this relatively more difficult.

 

Would appreciate input.

 

EDIT: Do you have a nagging suspicion that the dividends can't just be summed because their value depends on when they are paid out?  Time value of money thing.

[racemize]

I see the logic behind what you are doing; however, (and I know this will be a shocker), I lean towards the calculation that I perform, which has the advantage of telling you the price point where the warrant was better than buying the common in total returns.  Given the feedback I've gotten (or mostly lack thereof), I guess I'm the only person who thinks this way is valuable?  I guess it doesn't matter, since I'm the one using it...

 

Moreover, I don't really know how to use your number.  For example, if I plug in values for your cost of leverage, then I will come up with a point where the warrant's returns are higher than the common's returns (since yours returns a higher cost of leverage).  How would I then use that information in a meaningful way?

 

Let me be more specific, and I'll adjust to what you just posted:

 

Assumptions:

GM stock price: 40.16

GM warrant price: 22.41

GM strike price: 18.33

Assumed dividends: 0.3 over the next 22 quarters, for a total of 6.60 in dividends

 

Eric's method

amount borrowed = 40.16 - 22.41 - 6.60 = 11.15

gross return needed = 18.33 / 11.15 -1 = 64.3%

 

implied warrant price = 1.643*22.41 = 36.84

implied stock price at expiry from warrant = 36.84+18.33 = 55.17

total return of stock price given the implied stock price = (55.17+6.60)/40.16 = 53.8%

 

As you can see, the implied stock price results in an outcome where the warrant returns more than the total return of the stock price.  Thus, I do not think we have solved for the intersection point where the two returns are the same (I believe that was the point from you prior post)?  Perhaps I just don't understand what your cost of leverage means at this point, if it isn't that intersection point.

 

My method

Calculated Future Stock Price where the returns are equal: 49.81

Total return of common at that price = (49.81+6.60) / 40.16 = 40.46%

Total return of warrant at that price = (49.81-18.33-22.41)/22.41 = 40.47% (rounding)

 

 

Thus, you would annualize 53.8% of gains, and I would annualize 40.46% gains for the cost of leverage.  If yours is not where the total returns intersect, then what does it represent?

 

 

 

[racemize]

Or it could be this:

 

$17.75*1.x^5 = Y+$18.33

 

What's your opinion?

 

I did have a large beer at lunch which is making this relatively more difficult.

 

Would appreciate input.

 

Ok, I'll do the same analysis as the prior post for this formula and see what it spits out:

17.75*1.x = 6.6+18.33 = 24.93 ----> 40.4% gross return

 

This is exactly the same as my formula.  I think we have a winner.

 

Edit: Your formula is prettier/easier.  sadface.

[racemize]

EDIT: Do you have a nagging suspicion that the dividends can't just be summed because their value depends on when they are paid out?  Time value of money thing.

 

I do indeed have the suspicion.  No idea what to do with it though.

[ERICOPOLY]

Or it could be this:

 

$17.75*1.x^5 = Y+$18.33

 

What's your opinion?

 

I did have a large beer at lunch which is making this relatively more difficult.

 

Would appreciate input.

 

Ok, I'll do the same analysis as the prior post for this formula and see what it spits out:

17.75*1.x = 6.6+18.33 = 24.93 ----> 40.4% gross return

 

This is exactly the same as my formula.  I think we have a winner.

 

Edit: Your formula is prettier/easier.  sadface.

 

 

I'm glad it comes to the same result as yours.  Either it's right or we are both wrong.

 

My first iteration had at least one significant problem

 

1)  when Y was so big that it overwhelmed the number it was subtracted from -- that generates a negative number

 

 

[racemize]

The fact that it is definitely the intersection point of total returns should give us some confidence.

 

 

 

 

 

 

 

I think...

[txlaw]

But why are there different results between y'alls way and my way of calculating leverage?  Is it because the cost of leverage is a compound interest rate?

[ERICOPOLY]

EDIT: Do you have a nagging suspicion that the dividends can't just be summed because their value depends on when they are paid out?  Time value of money thing.

 

I do indeed have the suspicion.  No idea what to do with it though.

 

But I think your model also has the same mistake.  Because you don't do anything with your dividend, you're also effectively just summing it.  Instead, you could be reinvesting it in the stock in real time as it gets paid out.

 

[racemize]

EDIT: Do you have a nagging suspicion that the dividends can't just be summed because their value depends on when they are paid out?  Time value of money thing.

 

I do indeed have the suspicion.  No idea what to do with it though.

 

But I think your model also has the same mistake.  Because you don't do anything with your dividend, you're also effectively just summing it.  Instead, you could be reinvesting it in the stock in real time as it gets paid out.

 

I agree, I meant for both of them.

[racemize]

But why are there different results between y'alls way and my way of calculating leverage?  Is it because the cost of leverage is a compound interest rate?

 

I thought your way was an iteration back on Eric's--shouldn't you use Eric's new way to calculate it?

[gary17]

 

I suppose to be a bit more accurate one could calculate the present value of the dividends but given the dividend is a smaller number it probably doesn't make much difference.

 

So when a Co issues a dividend, do we add that to the strike or subtract it from the strike price. Thanks

 

 

 

Or it could be this:

 

$17.75*1.x^5 = Y+$18.33

 

What's your opinion?

 

I did have a large beer at lunch which is making this relatively more difficult.

 

Would appreciate input.

 

EDIT: Do you have a nagging suspicion that the dividends can't just be summed because their value depends on when they are paid out?  Time value of money thing.

[racemize]

I guess we could apply some reinvestment rate to the dividends, but then you would have to apply it uniformly.  Sounds like a nightmare.

[ERICOPOLY]

I have a feeling that it turns into one of the equations where you get the big greek Sigma letter in it.

[txlaw]

But why are there different results between y'alls way and my way of calculating leverage?  Is it because the cost of leverage is a compound interest rate?

 

I thought your way was an iteration back on Eric's--shouldn't you use Eric's new way to calculate it?

 

I don't think so.  They way I do it makes the most intuitive sense for calculating leverage to me. 

 

I think if Eric's way is right, our cost of leverage should come out the same (plus or minus NPV effects).  I think it might have to do with you guys using a compound interest rate.  But my brain is fried at this point.

[racemize]

But why are there different results between y'alls way and my way of calculating leverage?  Is it because the cost of leverage is a compound interest rate?

 

I thought your way was an iteration back on Eric's--shouldn't you use Eric's new way to calculate it?

 

I don't think so.  They way I do it makes the most intuitive sense for calculating leverage to me. 

 

I think if Eric's way is right, our cost of leverage should come out the same (plus or minus NPV effects).  I think it might have to do with you guys using a compound interest rate.  But my brain is fried at this point.

 

You and Eric are approaching it in a very different manner than I am, so I don't think I can comment too intelligently as to the way you are doing it.  Perhaps Eric can.

[ERICOPOLY]

But why are there different results between y'alls way and my way of calculating leverage?  Is it because the cost of leverage is a compound interest rate?

 

I thought your way was an iteration back on Eric's--shouldn't you use Eric's new way to calculate it?

 

I don't think so.  They way I do it makes the most intuitive sense for calculating leverage to me. 

 

I think if Eric's way is right, our cost of leverage should come out the same (plus or minus NPV effects).  I think it might have to do with you guys using a compound interest rate.  But my brain is fried at this point.

 

You and Eric are approaching it in a very different manner than I am, so I don't think I can comment too intelligently as to the way you are doing it.  Perhaps Eric can.

 

The compound interest rate is the right way to deal with the option premium (my first equation that I gave to Packer).  However, I think my attempts to modify it today are stuffed up.  By implication, since my second iteration today came to the same result as Racemize's spreadsheet, perhaps his spreadsheet too is stuffed up (if it comes to the same result).

 

And I think they are stuffed up for the reason that Racemize and I both suspected -- the summing up of the dividends.

 

We're acting like the missed dividend all comes at the end.  As if it were one huge whopping dividend payment missed at the very end of the term.  However, that's wrong, because the dividends are missed every step of the way. 

 

That meshes with txlaw's sustpicion that the error has to do with compounding rate.  We can't use the compounding rate to deal with the missed dividends because we are doing no adjustment for the time value of the missed dividends.

 

For example, $1 is 5% of $20.  But if you compound $20 by 5% for two years, you don't get $22.  Our methods of computing it therefore arrive at a different cost in the missing dividend scenario.

[racemize]

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.

[racemize]

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...

[ERICOPOLY]

That being said, I'm not sure that txlaw's method incorporates the missed compounding of dividends either--it seemed like it was just added at the end too...

 

I'm not sure how to overcome this issue.  Perhaps call it close enough, and no that it falls a little short.

 

I am only talking about how he deals with the cost of the lost dividend to the option.  He's just saying that it cost a percentage of the strike price. 

 

So let's say you borrow $10 (the strike price) and you miss a $1 dividend.  That's a 10% cost.

 

Compare that to borrowing $10 from your local banker at a 10% interest rate.  After a year, it cost you $1.

 

So he's right about that, I think.

 

The only time you have to worry about reinvestment of the dividend is when you are dealing with the common.  So it's a problem for you to overcome when you are fixing up your spreadsheet, but it's not something that txlaw has to deal with because he didn't take a stab at the common.

[ERICOPOLY]

Anyways, to be nitpicky a missed 25 cent dividend paid out quarterly does not have the same cost as a missed $1 dividend paid out annually.  However, I have only so much patience for being too exact.

[racemize]

Anyways, to be nitpicky a missed 25 cent dividend paid out quarterly does not have the same cost as a missed $1 dividend paid out annually.  However, I have only so much patience for being too exact.

 

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

 

 

[jeffmori7]

Guys, in the end, don't you think that what we have to guess from now on is : Will the appreciation of the stock price be more important than the total amount of dividend being payed over the 5 years by a fair amount ? If so, the warrants wins anyway, no matter the time value of money I would think.

 

At more than 1.2 times the dividend (which is the warrant to strike price ratio) in stock price appreciation, I think you win in all scenario.

[ERICOPOLY]

Here is another aspect of txlaw's calculation that differs:

 

Additionally, I have to pay pre-paid interest (the time premium) of $0.68 today. 

 

In order to get the nominal interest rate associated with the pre-paid interest, I have to solve for a rate that generates annual coupon payments with an NPV equal to the total amount of the pre-paid interest.  For simplicity's sake, let's say that comes out to 1% based on the discount rate I use.  And that rate, btw, should be keyed off the loan principal amount, aka the strike price.

 

 

I'm not sure if he recognized it, but the formula I provided to Packer solves for that.  It's a pretty easy formula to use.

 

Here is an easier phrasing:

 

You are prepaying all of this interest, long before it is due, which is effectively an interest-free loan to the very person you are borrowing it from.

 

Thus, you aren't really borrowing as much as you think.

 

Therefore, you have to figure out how much you are really borrowing first, before then calculating what interest rate you are really paying.

 

And that is an easy calculation.

 

Given:

BAC stock price $15.60

BAC "A" warrant price $6.54

Strike price $13.30

x= cost of leverage interest rate

 

$15.60 - $6.54 = $9.06

 

Now you need merely solve the following equation for 'x':

$9.06 * 1.x^5 = $13.30.

 

I'm using 5 years in the calculation to keep it simple, even though we're not exactly 5 years from expiry.

 

But that formula only tells you what the pre-paid interest really cost you -- it doesn't account for the cost of the lost dividends.