Mohnish Pabrai Boston College Presentation

[Packer16]

I think the results will be the same but my simple mind can't deal with more than one thing at a time.  That is why I marvel at ERICOPOLY's and others option calculations.  It reminds me when I was an undergrad EE and some folks could understand the wave theories and such as I was good at digital 1s and 0s but no much beyond that.

 

Packer

[Guest]

I know you guys are calulating the GM and BAC A warrants but is the cost of leverage on the AIG warrants around 10.6% now?

 

Following race's example

 

$74.95 (breakeven) / $49.55 (current stock price) = 1.51 * 7 (roughly 7 years left) = 10.58% Add a bit more for possible dividends. If this is right, isn't the quite a bit more expensive than it's been in the past?

 

I think your math is off once you hit 1.51.  From that number do the following:

 

1.52-1 = 52% raw gain needed to hit 74.95 from this point.  Annualzing that number is 5.98%.  Then, you can model dividends however you like.  The current dividend is 0.1, so all of those missed dividends adds from 74.95 to 76.07 (this uses yield and not raw missed dividends), which is the new break-even point, giving an annualized rate of 6.2%.  Alternatively, you could push all the way up to .17 (the threshold) since it will likely get to that point in the future, pushing 74.95 to 76.82 or 6.35% annualized.

 

ahh, cool. thanks man! :)

[ERICOPOLY]

In your quote there, you indicated that a 3% dividend equates to a 6% raise in cost of leverage if the warrant strike were 50% of stock; I'm a little confused there. 

 

Let's use an example where the stock is $36, the strike on the calls is $18, and the premium on the calls is $0.  So you can purchase the calls for $18 each (no premium).  Now, does it seem like the cost of leverage is 0%?  Not so fast!

 

You are basically "borrowing" $18 per share synthetically when the strike is $18, right?  You take your $36 in cash and buy two calls for $18 strike instead of purchasing 1 share of common for $36.

 

And you get no dividend, right?

 

So let's say the common is trading at $36, so the strike on the warrant is 50% of the cost of the stock -- just like I said.

 

Okay, 3% of $36 is $1.08 of dividend.

 

That's a dividend that you will miss out on, so it has to be added to the cost of getting that $18  worth of leverage.

 

$1.08 is 6% of $18.

 

Now, if you instead had used portfolio margin and purchased a put with $18 strike, you would not be losing the dividend.  So this kind of computation is only important to strategy where you lose the dividend (like with call option or warrant).

 

It's a real cost though.  The cost of leverage is not 0%, it's 6% in this example.

[racemize]

Well, I guess where I get confused is this:

 

I could have bought the 36 dollar stock and gotten the $1.08 dividend.

 

However, I could elect to buy two 18 dollar calls. 

 

Thus, it would seem I'm missing the $1.08 from 36, not from 18.  Or, in other words, I had no other investment choice where I could get 1.08 out of 18, so I'm not sure why I would divide by 18 to get 6% instead of 36 to get 3%. 

 

 

I do understand you could have gotten 6% if you had margined 100%, but presumably the puts would cost 3% more than the calls, which would again be a net loss of 3% for the calls, not 6%, right?

[gary17]

If you buy two 18 calls your committed to $72,.... no longer 36 so the dividend missed is more like 2

[Packer16]

You bring up a good point a current example are the FTR options as they have a high dividend.  The Jan 15s with a 4.50 SP are 40 cents. The current price in $4.56.  You will miss out in 45 dividends so the real cost is 79 cents (40+45-6 (in the moneyness)) divided by the SP ($4.50) is close to 18%.

 

Packer

[racemize]

You bring up a good point a current example are the FTR options as they have a high dividend.  The Jan 15s with a 4.50 SP are 40 cents. The current price in $4.56.  You will miss out in 45 dividends so the real cost is 79 cents (40+45-6 (in the moneyness)) divided by the SP ($4.50) is close to 18%.

 

Packer

 

This example makes more sense to me, but may be simply because the SP and the stock is similar.  It makes the most sense to me to use the dividend yield (annual dividend / stock price) as the additional cost for the dividend rather than dividing the dividend from the strike price. 

 

e.g., going back to Eric's example, there was no ability to invest $18 and get 1.08, it could only be gotten by investing $36. 

[ERICOPOLY]

I annuallize the (strike price + warrant price - stock price) / strike price over the remaining period of the warrant (5.12 years).

 

Packer

 

I see--I calculate it by figuring out where owning the warrants are better than owning the common and annualizing that number. 

 

For example, the point where the warrants make the same as the common is currently $22.94.  Thus, my rate is $22.94/$15.56, annualized, which is currently 7.9%, or since this is at parity, it would also be ($22.94-$13.30)/$6.54, or 7.9% annualized.  I also usually adjust for missed dividends, which adds be 0.01*remaining number of quarters to the $22.94 number, adjusting to 7.95% per year.  I'm not totally sure if that dividend adjustment is strictly the right way to do it, but it makes some sense (those are the raw dividends that were missed).

 

In your calculation, you are calculating how much extra your are paying now for the leverage (strike + warrant price - stock price), which makes sense.  Why then divide that by the strike?  Seems like you would want to divide by your cost (warrant price)? 

 

In any event, it seems like the first approach gives a slightly better indication of cost, since you could have bought the common instead of the option/warrant.  Is there an advantage to the second approach I'm missing?

 

Let's compare my method of calculating cost of leverage (over on the BAC Leverage thread) to Packer's method.

 

Packer's method comes out to a lower cost of leverage answer.

 

Why is that one might ask?

 

Simple...  well... sort of, anyhow  :)

 

You see, we're talking about pre-paying all of the "interest" on the synthetically borrowed money.  That's very different from a typical loan where you pay the interest incrementally as time goes by.

 

The difference is significant!  There is opportunity cost to settling up your interest costs on day one, versus day by day.  It's the time value of money.

 

Anyways, my method of calculating it is what I prefer to use because it compares apples-to-apples with the normal kind of loan where you pay interest on a rolling basis as the payments come due.

 

Make sense?

 

So that's the difference between my method and Packer's method.  His is perfectly fine for some things, but I find I can't make use of it for comparing one type of leverage (options) to another (borrowing money with normal interest payment).

 

My purpose was to compare various costs for all manner of leverage -- so it's why I do it that way and don't use Packer's method.  Packer's method of course is a lot easier to compute.

[ERICOPOLY]

If you buy two 18 calls your committed to $72,.... no longer 36 so the dividend missed is more like 2

 

We are thinking the same way, I just wasn't careful in how I described my example.

 

yes, two shares of upside.  two dividends missed.  twice we "borrowed" $18.  Thus, 1 missed dividend per $18 borrowed. 

 

Therefore, the missed dividend of 1.08 (per call) is 6% of the "borrowed" amount of $18 per call.

[racemize]

Ok, I'm still on the dividend issue.  Since a call misses dividends and a put doesn't (when paired with appropriate counterparts), one would expect there to be an implied dividend yield difference in cost.

 

So I looked at JPM Jan 15 calls/puts.  JPM has a 2.7% yield right now and is at 56.06.

 

The JPM Jan 15 57.5 call is 4.5.  Using (price + strike - stock price) / strike I get (4.5+57.5-56.06)/57.5 = 10.3% (using short method out of laziness

comparing to JPM Jan 15 57.5 put: price is 7.24.  So that cost is (7.24 - (57.5 - 56.06)) / 57.5 = 10.1%.

 

 

Ok so that failed.  Maybe I did something wrong.

 

I'll try out WFC, which is currently 44.11 with a 2.7% yield.

 

The WFC Jan 15 $45 call is 2.89.  So (2.89+45-44.11)/45 = 8.4%

The WFC Jan 15 $45 put is 4.85.  So (4.85 - (45 - 44.11))/45 = 8.8%

 

failed again.  Oh well.

 

 

 

[ERICOPOLY]

The BAC warrants will get a floor established to support the cost of leverage once a dividend is paid. 

 

Imagine if a $1 dividend were paid (it won't be that high, but just imagine).  That would be 7.5% of value versus what a regular call option offers.

 

So that large of a dividend, were it to be suddenly announced, would create quite a land grab for the warrants -- the price would spike right away.  They would suddenly be the best thing around, with effectively free options volatility premium (free embedded put) -- compared to a regular call options.  So for accounts that can't use margin loans  (like IRAs), it would be the best game in town and we'd see no more option decay.

[racemize]

If you buy two 18 calls your committed to $72,.... no longer 36 so the dividend missed is more like 2

 

We are thinking the same way, I just wasn't careful in how I described my example.

 

yes, two shares of upside.  two dividends missed.  twice we "borrowed" $18.  Thus, 1 missed dividend per $18 borrowed. 

 

Therefore, the missed dividend of 1.08 (per call) is 6% of the "borrowed" amount of $18 per call.

 

I get that 1.08 / 18 is 6%.  I just don't understand why we would think we should get the 1.08 in the first place.  If we had bought $18 of shares, we would have got a 3% yield, or .54.  If my choice was to buy the common unlevered or to buy the call, or some combination, nothing was going to give me a 6% yield, so why would I be missing that unattainable 6%?

[Packer16]

The approach I took was to say the value above the intrinsic value of the option was the equivalent of interest payments for the borrowed strike price.  This can be compared to other borrowing rates to see if it is cheap.  Others such as Greenblatt describe it this way in his book "You Can Be a Stock Market Genius" for LEAP calculations.  I think the results will be similar on a relative basis which is how I use it (in combination with option expected value calculations) and it is easier to calculate.  The calculation does not include the opportunity cost of investing in the stock but that is not what I use it for, I calculate the upside of the option and stock separately in a different calculation.  This requires 2 calculations but for me it is easier to see opportunities if I perform a separate calculations to estimate upside/downside.

 

Packer

[ERICOPOLY]

If you buy two 18 calls your committed to $72,.... no longer 36 so the dividend missed is more like 2

 

We are thinking the same way, I just wasn't careful in how I described my example.

 

yes, two shares of upside.  two dividends missed.  twice we "borrowed" $18.  Thus, 1 missed dividend per $18 borrowed. 

 

Therefore, the missed dividend of 1.08 (per call) is 6% of the "borrowed" amount of $18 per call.

 

I get that 1.08 / 18 is 6%.  I just don't understand why we would think we should get the 1.08 in the first place.  If we had bought $18 of shares, we would have got a 3% yield, or .54.  If my choice was to buy the common unlevered or to buy the call, or some combination, nothing was going to give me a 6% yield, so why would I be missing that unattainable 6%?

 

Example 1:  Using portfolio margin

Let's say I only have $18 to my name and I buy 1 share of common stock for $36 using $18 of money borrowed on margin.  I get dividend yield both on $18 of my own capital tied up and on $18 of the borrowed money

 

Example 2:  Using calls

I don't get a damn bit of dividend on my own $18 of equity, neither do I get a dividend on the $18 worth of synthetically "borrowed" money.

 

 

In Example 2, I not only miss out on dividend yield from the $18 borrowed, but I also miss out on the dividend yield from the $18 of my own equity that I contributed.

 

So that's why it's 6% cost and not 3% cost.  Because you synthetically borrowed only 1/2 the price of the stock, but you gave up the dividend on the entire thing!  Your own money got no yield.

 

Normally, if you invest your own $18 into the stock you get a 3% yield.  But that vanishes when you add $18 of "borrowed" money to the deal.  So you multiply it by 2, and thus it becomes a 6% cost of having added $18 of leverage.

[jay21]

If you buy two 18 calls your committed to $72,.... no longer 36 so the dividend missed is more like 2

 

We are thinking the same way, I just wasn't careful in how I described my example.

 

yes, two shares of upside.  two dividends missed.  twice we "borrowed" $18.  Thus, 1 missed dividend per $18 borrowed. 

 

Therefore, the missed dividend of 1.08 (per call) is 6% of the "borrowed" amount of $18 per call.

 

I get that 1.08 / 18 is 6%.  I just don't understand why we would think we should get the 1.08 in the first place.  If we had bought $18 of shares, we would have got a 3% yield, or .54.  If my choice was to buy the common unlevered or to buy the call, or some combination, nothing was going to give me a 6% yield, so why would I be missing that unattainable 6%?

 

Example 1:  Using portfolio margin

Let's say I only have $18 to my name and I buy 1 share of common stock for $36 using $18 of money borrowed on margin.  I get dividend yield both on $18 of my own capital tied up and on $18 of the borrowed money

 

Example 2:  Using calls

I don't get a damn bit of dividend on my own $18 of equity, neither do I get a dividend on the $18 worth of synthetically "borrowed" money.

 

 

In Example 2, I not only miss out on dividend yield from the $18 borrowed, but I also miss out on the dividend yield from the $18 of my own equity that I contributed.

 

So that's why it's 6% cost and not 3% cost.  Because you synthetically borrowed only 1/2 the price of the stock, but you gave up the dividend on the entire thing!  Your own money got no yield.

 

Normally, if you invest your own $18 into the stock you get a 3% yield.  But that vanishes when you add $18 of "borrowed" money to the deal.  So you multiply it by 2, and thus it becomes a 6% cost of having added $18 of leverage.

 

What yield premium should be applied to the secured liability to get to an apples to apples that you wanted?

[racemize]

Example 1:  Using portfolio margin

Let's say I only have $18 to my name and I buy 1 share of common stock for $36 using $18 of money borrowed on margin.  I get dividend yield both on $18 of my own capital tied up and on $18 of the borrowed money

 

I agree here, and it makes sense.  However, to be equivalent to the call version, you would have to buy puts at $18 right?  Wouldn't the puts be more expensive than the calls because of the implied dividend yield?  I tried to verify that earlier, but failed.  Is that just not right?  I was expecting it to work out due to put/call parity.

 

Example 2:  Using calls

I don't get a damn bit of dividend on my own $18 of equity, neither do I get a dividend on the $18 worth of synthetically "borrowed" money.

 

In Example 2, I not only miss out on dividend yield from the $18 borrowed, but I also miss out on the dividend yield from the $18 of my own equity that I contributed.

 

So that's why it's 6% cost and not 3% cost.  Because you synthetically borrowed only 1/2 the price of the stock, but you gave up the dividend on the entire thing!  Your own money got no yield.

 

Normally, if you invest your own $18 into the stock you get a 3% yield.  But that vanishes when you add $18 of "borrowed" money to the deal.  So you multiply it by 2, and thus it becomes a 6% cost of having added $18 of leverage.

 

I see what you are saying, but it just doesn't make much sense to me.  There was nothing that I could invest in, besides borrowing the margin and buying puts, that would have yielded 6% off of the dividends, and in that case, I still have the question above.

 

Let's put it another way.  I think I've calculated "cost of leverage" in the same way you do when there is no dividends.  Doing this allows me to know how much the common has to return for the warrant to break-even, or in other words, it allows me to directly compare at what point the warrant will return the same amount as the common. 

 

In the ridiculous case of $0 cost, the break even is right when I buy it, everything else is levered upside.  Let's say the price goes absolutely nowhere for a year, and a dividend of $1 is instituted.  Ok, now I need to make up for the $1 in total returns in having bought the warrant instead of buying the common, right?  So, the total return for the common is now 1/36 = 2.7%.  In order to break even with that, I need the warrant to go up to 18*1.027 = 18.5, or just $0.50 and not the $1.  So, it seems like if I "punish" the warrant by requiring a 5.4% yield or the full $1 dividend, it no longer provides the total return comparison I've been calculating.

 

Perhaps that means we just aren't calculating the same thing? 

 

[ERICOPOLY]

If you buy two 18 calls your committed to $72,.... no longer 36 so the dividend missed is more like 2

 

We are thinking the same way, I just wasn't careful in how I described my example.

 

yes, two shares of upside.  two dividends missed.  twice we "borrowed" $18.  Thus, 1 missed dividend per $18 borrowed. 

 

Therefore, the missed dividend of 1.08 (per call) is 6% of the "borrowed" amount of $18 per call.

 

I get that 1.08 / 18 is 6%.  I just don't understand why we would think we should get the 1.08 in the first place.  If we had bought $18 of shares, we would have got a 3% yield, or .54.  If my choice was to buy the common unlevered or to buy the call, or some combination, nothing was going to give me a 6% yield, so why would I be missing that unattainable 6%?

 

Example 1:  Using portfolio margin

Let's say I only have $18 to my name and I buy 1 share of common stock for $36 using $18 of money borrowed on margin.  I get dividend yield both on $18 of my own capital tied up and on $18 of the borrowed money

 

Example 2:  Using calls

I don't get a damn bit of dividend on my own $18 of equity, neither do I get a dividend on the $18 worth of synthetically "borrowed" money.

 

 

In Example 2, I not only miss out on dividend yield from the $18 borrowed, but I also miss out on the dividend yield from the $18 of my own equity that I contributed.

 

So that's why it's 6% cost and not 3% cost.  Because you synthetically borrowed only 1/2 the price of the stock, but you gave up the dividend on the entire thing!  Your own money got no yield.

 

Normally, if you invest your own $18 into the stock you get a 3% yield.  But that vanishes when you add $18 of "borrowed" money to the deal.  So you multiply it by 2, and thus it becomes a 6% cost of having added $18 of leverage.

 

What yield premium should be applied to the secured liability to get to an apples to apples that you wanted?

 

That's separated out into the price of the put used to secure the portfolio margin liability.

 

It's important, but a separate (related) topic.

 

Another separate but related topic is the risk of moving margin interest rate (another liability that is unsecured).

 

Those are important topics, but the dividend is a distinctly different threat, and it has a cost to the option holder.

[ERICOPOLY]

Example 1:  Using portfolio margin

Let's say I only have $18 to my name and I buy 1 share of common stock for $36 using $18 of money borrowed on margin.  I get dividend yield both on $18 of my own capital tied up and on $18 of the borrowed money

 

I agree here, and it makes sense.  However, to be equivalent to the call version, you would have to buy puts at $18 right?  Wouldn't the puts be more expensive than the calls because of the implied dividend yield?  I tried to verify that earlier, but failed.  Is that just not right?  I was expecting it to work out due to put/call parity.

 

There is no cost to the put.

 

The example, if you recall, is a $36 stock with $18 call strike price.

 

The call is priced at $18.

 

Thus, the embedded put in the call is free.

 

No, this isn't terribly realistic, but I wanted to keep the discussion on just the missing dividend.  So I reduced the complexity.

 

It is assumed (apples to apples) that the put is also free on the market (if it's free for the call).  Okay, not real-world, but I didn't want to get the discussion off track.  Too late!  :D

 

 

It's also the reason why I kept my example to one where the strike price was 1/2 of the stock price.  That way the math is very easy.  Just keeping complexity out of it so we can do these computations in our heads.

[racemize]

Example 1:  Using portfolio margin

Let's say I only have $18 to my name and I buy 1 share of common stock for $36 using $18 of money borrowed on margin.  I get dividend yield both on $18 of my own capital tied up and on $18 of the borrowed money

 

I agree here, and it makes sense.  However, to be equivalent to the call version, you would have to buy puts at $18 right?  Wouldn't the puts be more expensive than the calls because of the implied dividend yield?  I tried to verify that earlier, but failed.  Is that just not right?  I was expecting it to work out due to put/call parity.

 

There is no cost to the put.

 

The example, if you recall, is a $36 stock with $18 call strike price.

 

The call is priced at $18.

 

Thus, the embedded put in the call is free.

 

No, this isn't terribly realistic, but I wanted to keep the discussion on just the missing dividend.  So I reduced the complexity.

 

It is assumed (apples to apples) that the put is also free on the market (if it's free for the call).  Okay, not real-world, but I didn't want to get the discussion off track.  Too late!  :D

 

Sure. 

 

If we did go ahead and assume a dividend, wouldn't the put cost more by the dividend yield amount than the call though?  That was what I was trying to calculate with the JPM and WFC examples, but it didn't work out that way, or at least didn't seem to.

[ERICOPOLY]

Wouldn't the puts be more expensive than the calls because of the implied dividend yield?  I tried to verify that earlier, but failed.  Is that just not right?  I was expecting it to work out due to put/call parity.

 

I didn't engage because it was getting off track.

 

What interest rate did you use?  There is $18 being "borrowed" in the case of the call, but not in the case of the put.  Did you omit that expense from the call?

 

[racemize]

Wouldn't the puts be more expensive than the calls because of the implied dividend yield?  I tried to verify that earlier, but failed.  Is that just not right?  I was expecting it to work out due to put/call parity.

 

I didn't engage because it was getting off track.

 

What interest rate did you use?  There is $18 being "borrowed" in the case of the call, but not in the case of the put.  Did you omit that expense from the call?

 

You're right, I'm more interested in the other half of the discussion.  I was just thinking that since calls don't get the dividend on one side and the puts + stock do, then the puts would necessarily be more expensive than the calls.  It would depend on the bond yield, so that's probably why the dividend yield didn't matter that much.  Still, though, if one can get double the dividend by margining + puts, it would seem like the puts price should reflect that difference in possibility. 

 

I'll focus back on the other conversation though.

[ERICOPOLY]

Wouldn't the puts be more expensive than the calls because of the implied dividend yield?  I tried to verify that earlier, but failed.  Is that just not right?  I was expecting it to work out due to put/call parity.

 

I didn't engage because it was getting off track.

 

What interest rate did you use?  There is $18 being "borrowed" in the case of the call, but not in the case of the put.  Did you omit that expense from the call?

 

You're right, I'm more interested in the other half of the discussion.  I was just thinking that since calls don't get the dividend on one side and the puts + stock do, then the puts would necessarily be more expensive than the calls.  It would depend on the bond yield, so that's probably why the dividend yield didn't matter that much.  Still, though, if one can get double the dividend by margining + puts, it would seem like the puts price should reflect that difference in possibility. 

 

I'll focus back on the other conversation though.

 

In November I bought BAC A warrants again in our RothIRA accounts.  My thinking was around the 7.5% cost of leverage (waaaayyyyy cheaper than in March), and the prospects for the dividend coming soon, and the relative convenience of "one and done" trading for the next 5 years.  Having a Roth account is a trading liability because I run the risk of losing my taxable losses if they wash into a Roth trade - so I am very careful about managing that risk.  Anyways, that wash period is over soon (then I can take the taxable loss on my expiring puts).

 

Let's say BAC pays a 60 cent dividend (in 2015 or 2016) -- that would be 4.5% cost of leverage justification in those A warrants.  Then let's say 2% cost for the put and 1% cost for the margin loan.  That adds up to the cost of leverage in the A warrants at 7.5% rate.

 

So they look like they are attractively price, IMO.  I aggressively moved into them in November.

[twacowfca]

If you buy two 18 calls your committed to $72,.... no longer 36 so the dividend missed is more like 2

 

We are thinking the same way, I just wasn't careful in how I described my example.

 

yes, two shares of upside.  two dividends missed.  twice we "borrowed" $18.  Thus, 1 missed dividend per $18 borrowed. 

 

Therefore, the missed dividend of 1.08 (per call) is 6% of the "borrowed" amount of $18 per call.

 

I get that 1.08 / 18 is 6%.  I just don't understand why we would think we should get the 1.08 in the first place.  If we had bought $18 of shares, we would have got a 3% yield, or .54.  If my choice was to buy the common unlevered or to buy the call, or some combination, nothing was going to give me a 6% yield, so why would I be missing that unattainable 6%?

 

Example 1:  Using portfolio margin

Let's say I only have $18 to my name and I buy 1 share of common stock for $36 using $18 of money borrowed on margin.  I get dividend yield both on $18 of my own capital tied up and on $18 of the borrowed money

 

Example 2:  Using calls

I don't get a damn bit of dividend on my own $18 of equity, neither do I get a dividend on the $18 worth of synthetically "borrowed" money.

 

 

In Example 2, I not only miss out on dividend yield from the $18 borrowed, but I also miss out on the dividend yield from the $18 of my own equity that I contributed.

 

So that's why it's 6% cost and not 3% cost.  Because you synthetically borrowed only 1/2 the price of the stock, but you gave up the dividend on the entire thing!  Your own money got no yield.

 

Normally, if you invest your own $18 into the stock you get a 3% yield.  But that vanishes when you add $18 of "borrowed" money to the deal.  So you multiply it by 2, and thus it becomes a 6% cost of having added $18 of leverage.

 

Yup. But if the writer of the call borrowed money as in example #1 and used it to write a covered call, that double dividend would influence him to  charge less for writing that call, especially compared to writing a put where posting a compensating balance would earn almost nothing --- thus leading to demanding a higher price for writing an equivalent put.

[ERICOPOLY]

The approach I took was to say the value above the intrinsic value of the option was the equivalent of interest payments for the borrowed strike price.  This can be compared to other borrowing rates to see if it is cheap.  Others such as Greenblatt describe it this way in his book "You Can Be a Stock Market Genius" for LEAP calculations.  I think the results will be similar on a relative basis which is how I use it (in combination with option expected value calculations) and it is easier to calculate.  The calculation does not include the opportunity cost of investing in the stock but that is not what I use it for, I calculate the upside of the option and stock separately in a different calculation.  This requires 2 calculations but for me it is easier to see opportunities if I perform a separate calculations to estimate upside/downside.

 

Packer

 

 

Think of an individual with a steady job but not a penny to his name, getting a zero-money-down 5 year term $20,000 car loan that is interest-only and a balloon payment is due at the end of 5 years.  I know, I know, suspend your disbelief for a moment.

 

I believe it is a better loan for this consumer to pay the interest monthly as it accrues.  That's the whole reason why they wanted a loan in the first place -- they have no immediate cash and need to borrow.  They can't prepay it.

 

Instead, suppose they have to prepay all of the interest.  Okay, that's $5,000 in future interest that's due immediately before they can drive the car off of the lot.  But they don't have $5,000.  So they have to borrow it.  And you aren't including the cost of borrowing it in your calculation.

 

Borrowing it costs more money!  And that's an easy way to see that the loan is more expensive than your (and Greenblatt's) calculation suggests).

 

 

Back to our options & warrants...  you effectively have to "borrow" more because you have less equity with which to purchase the stock after pre-paying all of that interest upfront. 

 

Or looked at differently, you are giving the lender an interest-free loan (by prepaying interest long before it's due) and carrying on as if handing out interest-free loans has no economic cost.

 

So anyways, I think Greenblatt is incorrect.  The calculation that I make really isn't that hard, and it's accurate at the same time.

[ERICOPOLY]

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.