On Leverage

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grayfox
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Re: On Leverage

Post by grayfox » Thu Mar 14, 2019 6:33 am

pezblanco wrote:
Wed Mar 13, 2019 8:02 pm

The most basic strategy is just to leverage up stocks right? ... LEAPS are just long options on any index, not just the S&P500. I've been doing some calculations and basically you can borrow money using LEAPS for around 3.5% nominal right now. It is a little tricky to compute the borrowing rate since the dividends being paid in the future aren't known exactly (or guaranteed). So if inflation is 2.5% then you can borrow at 1% real. The S&P should give you at least 5% real (long term it has given 7% real) going forward from our high valuations. So, that gives you your 4% real cushion. Shouldn't you be pulling the trigger on this, Grayfox? :D
The only problem is, I don't really understand how LEAPS work. I just know that they are some kind of call option. And how long? Can you get them for 10 or 20 years?

I did buy options once a long time ago, but have forgotten all the details about how they work. I also tried selling covered calls a couple of times. I just remember there was a pricing model that took into account how much time was left to go and how volatile the stock was.

:?: What I don't get is how is buying options the same as borrowing money to buy stocks? I don't see how this two things are equated. Buying LEAPS sounds more like options trading than leveraging stocks. And which options do you buy? out-of-the-money, in-the-money? It seems like it would be a very complicated analysis.

The only reason I would be interested in LEAPS is because Zvi Bodie is behind the idea, and he is very wise professor and also promotes very low risk investing. So there must be something worthwhile to it.

alex_686
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Re: On Leverage

Post by alex_686 » Thu Mar 14, 2019 10:12 am

grayfox wrote:
Thu Mar 14, 2019 6:33 am
The only problem is, I don't really understand how LEAPS work. I just know that they are some kind of call option. And how long? Can you get them for 10 or 20 years? ... :?: What I don't get is how is buying options the same as borrowing money to buy stocks? I don't see how this two things are equated. Buying LEAPS sounds more like options trading than leveraging stocks. And which options do you buy? out-of-the-money, in-the-money? It seems like it would be a very complicated analysis.
LEAPs are any option with a time frame of longer than 9 months. IIRC, Warren Buffet wrote some custom over-the-counter S&P options with a life of 10 year. Options that expire on January 1st for the next 2 to 3 calendar years are more commonalty traded on the exchange.

When you are buying a option you are really paying for time and volatility. Time being at the risk free rate. So what you do is buy some long dated out of the money options. If the market goes up it pays off big. If the market goes down you lose your premium. It is not a perfect replication of a leverage model and modeling its behavior is harder, and back-testing is statistically worthless. But it is in the same ballpark as a leverage portfolio.

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pezblanco
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Re: On Leverage

Post by pezblanco » Thu Mar 14, 2019 11:19 am

alex_686 wrote:
Thu Mar 14, 2019 10:12 am
grayfox wrote:
Thu Mar 14, 2019 6:33 am
The only problem is, I don't really understand how LEAPS work. I just know that they are some kind of call option. And how long? Can you get them for 10 or 20 years? ... :?: What I don't get is how is buying options the same as borrowing money to buy stocks? I don't see how this two things are equated. Buying LEAPS sounds more like options trading than leveraging stocks. And which options do you buy? out-of-the-money, in-the-money? It seems like it would be a very complicated analysis.
LEAPs are any option with a time frame of longer than 9 months. IIRC, Warren Buffet wrote some custom over-the-counter S&P options with a life of 10 year. Options that expire on January 1st for the next 2 to 3 calendar years are more commonalty traded on the exchange.

When you are buying a option you are really paying for time and volatility. Time being at the risk free rate. So what you do is buy some long dated out of the money options. If the market goes up it pays off big. If the market goes down you lose your premium. It is not a perfect replication of a leverage model and modeling its behavior is harder, and back-testing is statistically worthless. But it is in the same ballpark as a leverage portfolio.
What is usually suggested is to not try to play the option gambling game and buy options (LEAPS) that are DEEP in the money. So, for example, the SPDR S&P 500 ETF is at around 280 right now. If you wanted about 2 to 1 leverage you would buy an option with strike price of around 140.

alex_686
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Re: On Leverage

Post by alex_686 » Thu Mar 14, 2019 11:40 am

pezblanco wrote:
Thu Mar 14, 2019 11:19 am
What is usually suggested is to not try to play the option gambling game and buy options (LEAPS) that are DEEP in the money. So, for example, the SPDR S&P 500 ETF is at around 280 right now. If you wanted about 2 to 1 leverage you would buy an option with strike price of around 140.
Eh - Maybe. There are valid arguments to make for out of the money, at the money, or in the money. All should increase the Beta's of one portfolio. The problem with deep in the money is that they are expensive. They require a higher upfront outlay of capital. They have a higher bid-ask spread. And then there is the volatility smile. On the plus side their Delta and Gamma values are closer to leveraging a portfolio with margin. I would probably go something closer to at the money or slightly out of the money - but that almost deserves a whole new topic.

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pezblanco
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Re: On Leverage

Post by pezblanco » Thu Mar 14, 2019 2:52 pm

alex_686 wrote:
Thu Mar 14, 2019 11:40 am
pezblanco wrote:
Thu Mar 14, 2019 11:19 am
What is usually suggested is to not try to play the option gambling game and buy options (LEAPS) that are DEEP in the money. So, for example, the SPDR S&P 500 ETF is at around 280 right now. If you wanted about 2 to 1 leverage you would buy an option with strike price of around 140.
Eh - Maybe. There are valid arguments to make for out of the money, at the money, or in the money. All should increase the Beta's of one portfolio. The problem with deep in the money is that they are expensive. They require a higher upfront outlay of capital. They have a higher bid-ask spread. And then there is the volatility smile. On the plus side their Delta and Gamma values are closer to leveraging a portfolio with margin. I would probably go something closer to at the money or slightly out of the money - but that almost deserves a whole new topic.
Alex, there is no question you know more about options and trading options than I do.

I just did a quick calculation on borrowing costs of the Jan 15, 2021 LEAP: Using Yahoo Finance and the SPDR Option Chain Data.

For the 140 Strike, the implied borrowing cost on the last trade made is 3.9%
For the 280 Strike, the implied borrowing cost on the last trade made is 7.5%

You paying for and getting something extra with the 280 strike price ... most obviously you're getting lots of downside protection. That has to be paid for.

alex_686
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Re: On Leverage

Post by alex_686 » Thu Mar 14, 2019 3:20 pm

pezblanco wrote:
Thu Mar 14, 2019 2:52 pm
You paying for and getting something extra with the 280 strike price ... most obviously you're getting lots of downside protection. That has to be paid for.
Can you walk me through you calculations? What you are saying does not square with the more formal models that I have been trained - like Black-Scholes or the Binomial Model. I will tell you what my guess is. I don't think it is any type of downside protection.

For the $140 strike you are getting more or less the time-value of the stock - just like leverage. So it is basically the risk free rate. It is a little bit dirty because of the bid/ask spreads and delays between various pricing services.

The $280 is evenly split between the time-value of the stock and the cost of volatility. The $140 is going to have a more or less symmetric pay off like a leverage portfolio. The $280 is either going to lose it all (all of the premium) or is going to be a massive payoff.

ThrustVectoring
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Re: On Leverage

Post by ThrustVectoring » Thu Mar 14, 2019 3:46 pm

alex_686 wrote:
Thu Mar 14, 2019 3:20 pm
pezblanco wrote:
Thu Mar 14, 2019 2:52 pm
You paying for and getting something extra with the 280 strike price ... most obviously you're getting lots of downside protection. That has to be paid for.
Can you walk me through you calculations? What you are saying does not square with the more formal models that I have been trained - like Black-Scholes or the Binomial Model. I will tell you what my guess is. I don't think it is any type of downside protection.

For the $140 strike you are getting more or less the time-value of the stock - just like leverage. So it is basically the risk free rate. It is a little bit dirty because of the bid/ask spreads and delays between various pricing services.

The $280 is evenly split between the time-value of the stock and the cost of volatility. The $140 is going to have a more or less symmetric pay off like a leverage portfolio. The $280 is either going to lose it all (all of the premium) or is going to be a massive payoff.
Put-call parity is the math for this. Long call + short put = time-discounted future price above the strike price. For very rough analysis you can ignore time discounting and dividends and just use "underlying price - strike price" on the right hand side and have a model that's good enough for general decision-making but not arbitrage.

So the "downside protection" is from neglecting to sell the put option at the same strike and expiration when you go from the underlying to the call option + cash. At the $280 strike, the value of the put option that you're implicitly buying (via not selling it) is significant. At the $140 strike, it's minimal.

Of course, if you're going synthetic long via options, you could always get the exact same effect out of just taking out a futures contract instead. And because of the arbitrage math of put-call parity, you effectively are, you're just paying a market-making arbitrageur for the privilege of having it as a long option instead of a futures contract.
Current portfolio: 60% VTI / 40% VXUS

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pezblanco
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Re: On Leverage

Post by pezblanco » Thu Mar 14, 2019 4:34 pm

Lets take a look at the Jan 15, 2021 SPDR LEAP with strike 140.

Data on last trade:

Date of Last Trade: 2/26/2019

Option Price of Last Trade: 139.36

Index value on that date: High 280.3 Low 278.9 %I just take the average of these = (279.6)

Implied Amount Borrowed (iab): IndexValue - OptionPrice: 140.24

Last Quarterly Value of Spyder dividend: 1.419

Days till Expiration (de): 689

Foregone dividends: There are 8 dividend dates in the range ... so 1.419*8 = 11.352 %these dividends should be discounted back to the present day using the inflation rate but that just changes things a few cents.

Transaction Costs per share: .0630 %You can buy a contract for $3.15 so for roundtrip and per share,

You buy the option and say immediately exercise it. How much do you end up with? You get (Index - Strike) - OptionPrice. This is usually a negative number. So that is an extra implied payment. So in this case, the extra implied payment is: -.24 (it turns out negative this time!). I think this comes about from me not knowing the exact index value at the purchase time?

Total Implied Payment (tip): 11.352 + .0630 + (-.24) = 11.175

Thus, the interest rate in percent is given by the formula:

interest rate =100*((exp((365/de)*(log((tip+iab)/iab)))) - 1) = 4.145

(I should add, this is basically the method used in Ayres & Nalebuff to do this calculation ... i.e. it's not my own invention)

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pezblanco
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Re: On Leverage

Post by pezblanco » Thu Mar 14, 2019 4:49 pm

ThrustVectoring wrote:
Thu Mar 14, 2019 3:46 pm
alex_686 wrote:
Thu Mar 14, 2019 3:20 pm
pezblanco wrote:
Thu Mar 14, 2019 2:52 pm
You paying for and getting something extra with the 280 strike price ... most obviously you're getting lots of downside protection. That has to be paid for.
Can you walk me through you calculations? What you are saying does not square with the more formal models that I have been trained - like Black-Scholes or the Binomial Model. I will tell you what my guess is. I don't think it is any type of downside protection.

For the $140 strike you are getting more or less the time-value of the stock - just like leverage. So it is basically the risk free rate. It is a little bit dirty because of the bid/ask spreads and delays between various pricing services.

The $280 is evenly split between the time-value of the stock and the cost of volatility. The $140 is going to have a more or less symmetric pay off like a leverage portfolio. The $280 is either going to lose it all (all of the premium) or is going to be a massive payoff.
Put-call parity is the math for this. Long call + short put = time-discounted future price above the strike price. For very rough analysis you can ignore time discounting and dividends and just use "underlying price - strike price" on the right hand side and have a model that's good enough for general decision-making but not arbitrage.

So the "downside protection" is from neglecting to sell the put option at the same strike and expiration when you go from the underlying to the call option + cash. At the $280 strike, the value of the put option that you're implicitly buying (via not selling it) is significant. At the $140 strike, it's minimal.

Of course, if you're going synthetic long via options, you could always get the exact same effect out of just taking out a futures contract instead. And because of the arbitrage math of put-call parity, you effectively are, you're just paying a market-making arbitrageur for the privilege of having it as a long option instead of a futures contract.
Thank you! A much more elegant way to explain what I was calling "downside protection"!

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grayfox
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Re: On Leverage

Post by grayfox » Fri Mar 15, 2019 10:34 am

pezblanco wrote:
Thu Mar 14, 2019 11:19 am

What is usually suggested is to not try to play the option gambling game and buy options (LEAPS) that are DEEP in the money. So, for example, the SPDR S&P 500 ETF is at around 280 right now. If you wanted about 2 to 1 leverage you would buy an option with strike price of around 140.
Right this second SPY = 2820.35 x 100 = 28,203.50
SPY Jun 2019 140.000 call shows
BID 141.33
ASK 141.64

If you bought at ASK, 141.64 x 100 = 14,164.00 + commission (assume no commissions)
So you are "borrowing" 28,203.50 - 14,164.00 = 14,013.50 ?
What is the interest rate?

This stops trading June 21, 2019 Options Expiration Calendar 2019

If on June 21, SPY ends up exactly where it is today, 2820.35
then you can buy at 14,000 and sell it at 28,203.50 for a difference of 14,203.50 ?
Since you paid 14,164.00, so you made $39.50 profit?
That sounds like interest rate was negative. That can't be right.

:!: Also, it has been mentioned that you don't receive dividends during that time. You only get the price increase.

Here is the LEAP: SPY Dec 2021 140.000 call
Bid 140.52
Ask 144.12
Much wider spread than for the June 2019!

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305pelusa
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Re: On Leverage

Post by 305pelusa » Fri Mar 15, 2019 10:51 am

grayfox wrote:
Fri Mar 15, 2019 10:34 am
pezblanco wrote:
Thu Mar 14, 2019 11:19 am

What is usually suggested is to not try to play the option gambling game and buy options (LEAPS) that are DEEP in the money. So, for example, the SPDR S&P 500 ETF is at around 280 right now. If you wanted about 2 to 1 leverage you would buy an option with strike price of around 140.
Right this second SPY = 2820.35 x 100 = 28,203.50
SPY Jun 2019 140.000 call shows
BID 141.33
ASK 141.64

If you bought at ASK, 141.64 x 100 = 14,164.00 + commission (assume no commissions)
So you are "borrowing" 28,203.50 - 14,164.00 = 14,013.50 ?
What is the interest rate?

This stops trading June 21, 2019 Options Expiration Calendar 2019

If on June 21, SPY ends up exactly where it is today, 2820.35
then you can buy at 14,000 and sell it at 28,203.50 for a difference of 14,203.50 ?
Since you paid 14,164.00, so you made $39.50 profit?

Here is the LEAP: SPY Dec 2021 140.000 call
Bid 140.52
Ask 144.12
One small correction. What you "borrow" is the strike price. That's what you'll have to pay in the future but are being allowed to not pay yet even though you have exposure to the full stock price.

Yes, if the stock price stayed as-is, you'd appear to make a 39 dollar profit. That's what happens when the ask+strike price are lower than the actual stock price.

You'd have to account for dividends not received. At 1.9% dividend yield annually, that's 535 bucks for the whole year (at a price of 28203). It's only 3 months though so that's a loss of 134 dollars

Subtract 134 from your "gain" of 39, for a total cost of 95 dollars. Paying 95 dollars to borrow 14000 for 3 months annualizes to ~2.7% borrowing rate.

If anyone can confirm this math, that'd be great

alex_686
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Re: On Leverage

Post by alex_686 » Fri Mar 15, 2019 11:17 am

A couple of points.

If you are interested in going down this route, I would urge you to read up on the formal theory of option pricing. Focus on pricing volatility, such as the VIX. Then focus on the Greeks - delta, gamma, theta, and vega.

Next, ignore dividends. They are just not that germane to your question. You are not buying the dividends, thus including them is like comparing apples to oranges. Also, the interest rate is the risk free rate - both in theory and almost universally true in practice. I understand what you are trying to do here - it is intuitive. It just not a very fruitful line of attack.

Next, to put the put-call parity in the proper context, you need to know the correct / intrinsic price of the put or the call to actually use it for what you are trying to do. Elsewise it is just a arbitrage trade.
Last edited by alex_686 on Fri Mar 15, 2019 11:34 am, edited 1 time in total.

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pezblanco
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Re: On Leverage

Post by pezblanco » Fri Mar 15, 2019 11:33 am

grayfox wrote:
Fri Mar 15, 2019 10:34 am
pezblanco wrote:
Thu Mar 14, 2019 11:19 am

What is usually suggested is to not try to play the option gambling game and buy options (LEAPS) that are DEEP in the money. So, for example, the SPDR S&P 500 ETF is at around 280 right now. If you wanted about 2 to 1 leverage you would buy an option with strike price of around 140.
Right this second SPY = 2820.35 you mean 282.35 x 100 = 28,203.50
SPY Jun 2019 140.000 call shows
BID 141.33
ASK 141.64

If you bought at ASK, 141.64 x 100 = 14,164.00 + commission (assume no commissions)
So you are "borrowing" 28,203.50 - 14,164.00 = 14,013.50 ? yes
What is the interest rate?

OK, so we have to calculate the true cost of borrowing. In this period I count (please check for me) that we miss 9 dividend payments:
So just using 2018 dividend payments on SPY: https://seekingalpha.com/symbol/SPY/dividends/history we get that we lose

$11.6362 of dividends. We lose $.0630 transaction costs per share and the implied extra payment is -$.395 (which is again negative!). So total cost of borrowing is $11.3042 per share. The number of days until expiration is 829. So, we know how much we are borrowing and for how long and how much it costs so we can compute the interest rate which is 3.47% in this case.


This stops trading June 21, 2019 Options Expiration Calendar 2019

If on June 21, SPY ends up exactly where it is today, 2820.35
then you can buy at 14,000 and sell it at 28,203.50 for a difference of 14,203.50 ? Yes
Since you paid 14,164.00, so you made $39.50 profit? Yes
That sounds like interest rate was negative. That can't be right. But you tied up 14,164 for 829 days. If you could have gotten say 3% interest on that money, you would have received $983, which you now don't have.

:!: Also, it has been mentioned that you don't receive dividends during that time. You only get the price increase. Correct

Here is the LEAP: SPY Dec 2021 140.000 call
Bid 140.52
Ask 144.12
Much wider spread than for the June 2019!

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pezblanco
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Re: On Leverage

Post by pezblanco » Fri Mar 15, 2019 11:39 am

305pelusa wrote:
Fri Mar 15, 2019 10:51 am
grayfox wrote:
Fri Mar 15, 2019 10:34 am
pezblanco wrote:
Thu Mar 14, 2019 11:19 am

What is usually suggested is to not try to play the option gambling game and buy options (LEAPS) that are DEEP in the money. So, for example, the SPDR S&P 500 ETF is at around 280 right now. If you wanted about 2 to 1 leverage you would buy an option with strike price of around 140.
Right this second SPY = 2820.35 x 100 = 28,203.50
SPY Jun 2019 140.000 call shows
BID 141.33
ASK 141.64

If you bought at ASK, 141.64 x 100 = 14,164.00 + commission (assume no commissions)
So you are "borrowing" 28,203.50 - 14,164.00 = 14,013.50 ?
What is the interest rate?

This stops trading June 21, 2019 Options Expiration Calendar 2019

If on June 21, SPY ends up exactly where it is today, 2820.35
then you can buy at 14,000 and sell it at 28,203.50 for a difference of 14,203.50 ?
Since you paid 14,164.00, so you made $39.50 profit?

Here is the LEAP: SPY Dec 2021 140.000 call
Bid 140.52
Ask 144.12
One small correction. What you "borrow" is the strike price. That's what you'll have to pay in the future but are being allowed to not pay yet even though you have exposure to the full stock price. According to Ayres and Nalebuff, what you are borrowing is the difference between the current value of underlying and the amount that you have paid (the option price). I understand what you are saying but you are actually borrowing a little more than the strike price. The "borrow costs" are being rolled into the loan is one way to think about it.

Yes, if the stock price stayed as-is, you'd appear to make a 39 dollar profit. That's what happens when the ask+strike price are lower than the actual stock price.

You'd have to account for dividends not received. At 1.9% dividend yield annually, that's 535 bucks for the whole year (at a price of 28203). It's only 3 months though so that's a loss of 134 dollars

Subtract 134 from your "gain" of 39, for a total cost of 95 dollars. Paying 95 dollars to borrow 14000 for 3 months annualizes to ~2.7% borrowing rate.

If anyone can confirm this math, that'd be great

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pezblanco
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Re: On Leverage

Post by pezblanco » Fri Mar 15, 2019 11:42 am

alex_686 wrote:
Fri Mar 15, 2019 11:17 am
A couple of points.

If you are interested in going down this route, I would urge you to read up on the formal theory of option pricing. Focus on pricing volatility, such as the VIX. Then focus on the Greeks - delta, gamma, theta, and vega.

Next, ignore dividends. They are just not that germane to your question. You are not buying the dividends, thus including them is like comparing apples to oranges. Also, the interest rate is the risk free rate - both in theory and almost universally true in practice. I understand what you are trying to do here - it is intuitive. It just not a very fruitful line of attack.

Next, to put the put-call parity in the proper context, you need to know the correct / intrinsic price of the put or the call to actually use it for what you are trying to do. Elsewise it is just a arbitrage trade.
Alex, I think that one way to interpret all this is to note that you actually are buying the dividends. The dividends are huge here in the context of calculating the true borrowing costs. The greeks of the options are almost superfluous for this application of buying deep in the money LEAPS and holding them till expiration

alex_686
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Re: On Leverage

Post by alex_686 » Fri Mar 15, 2019 12:11 pm

pezblanco wrote:
Fri Mar 15, 2019 11:42 am
Alex, I think that one way to interpret all this is to note that you actually are buying the dividends. The dividends are huge here in the context of calculating the true borrowing costs. The greeks of the options are almost superfluous for this application of buying deep in the money LEAPS and holding them till expiration
Pezblanco, can you expound on the dividends portion a bit more? You (mostly) don't get the dividends from options. Since you are not buying them, what impact should they have in the calculations?

I do think the Greeks are important in this conversation. If you know the Greeks you can figure out what role interest and dividends have on option pricing - which is limited. And if Greeks are superfluous at $140, are they also superfluous also at $200? 220? 240? So less of an outlay of initial capital for the same market exposure - right? I suspect that $140 was chosen because it is 50% of $280, and most margin calculation start at 50% margin borrowing. So it makes intuitive sense, but maybe not really that applicable to terms of math. Maybe we could find some other option which has the same market exposure and narrower bid/ask spreads?

DonIce
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Re: On Leverage

Post by DonIce » Fri Mar 15, 2019 1:26 pm

Just use futures. Simpler and cheaper.

PluckyDucky
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Re: On Leverage

Post by PluckyDucky » Fri Mar 15, 2019 1:56 pm

grayfox wrote:
Wed Mar 13, 2019 6:58 am
That could be a thread by itself to debate whether high inflation is off the table because of a paradigm shift in monetary policy. This would interest a lot of Bogleheads considering that its commonly recommended that half of bonds should be inflation-indexed bonds. I'm sure grok would be glad to hear that he can sell all his TIPS.

Meanwhile, I see that there is a third leverage strategy. Just to review:

First is leverage up low volatility portfolio like 40/60 until it has similar risk as 100% stocks. E.g. 2x or 3x 40/60 with Leveraged ETFs. Possibility to double the return of S&P500. But this maintains the same high-risk portfolio forever, so when/if the risk shows up you are guaranteed to experience deep drawdowns.

Second is the Ayres & Nalebuff Lifecycle investing which sounds like age-in-bonds on steroids. Start with something like 200/0/-100 and end up with 40/60/0. This has the benefit that it gets less risky over time. If you are lucky, you will be de-levereged when the risk does show up.

The third I'm seeing is Zvi Bodie's 90% TIPS / 10% LEAPS discussed here. Apparently LEAPS are call options on S&P500. I think they are for 3-years. Somehow, a call option acts like leverage. This sounds like the least risky approach to using leverage.** How would you backtest that with portviz?

** Maybe not. It sounds like you can loose 10% every time your call options expire worthless. Death by 1,000 cuts.
Options are fun. An in the money option will move (usually) dollar for dollar with the underlying. BUT the option costs less than the underlying, so the % move is greater.

Option contracts are usually for 100 shares. That is how it is leveraged. I pay $10 to command 100 shares that could be $100 each.

The downside is that options expire. But you should either roll them over, sell them, or exercise them before expiration.

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pezblanco
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Re: On Leverage

Post by pezblanco » Fri Mar 15, 2019 2:37 pm

alex_686 wrote:
Fri Mar 15, 2019 12:11 pm
pezblanco wrote:
Fri Mar 15, 2019 11:42 am
Alex, I think that one way to interpret all this is to note that you actually are buying the dividends. The dividends are huge here in the context of calculating the true borrowing costs. The greeks of the options are almost superfluous for this application of buying deep in the money LEAPS and holding them till expiration
Pezblanco, can you expound on the dividends portion a bit more? You (mostly) don't get the dividends from options. Since you are not buying them, what impact should they have in the calculations?

I do think the Greeks are important in this conversation. If you know the Greeks you can figure out what role interest and dividends have on option pricing - which is limited. And if Greeks are superfluous at $140, are they also superfluous also at $200? 220? 240? So less of an outlay of initial capital for the same market exposure - right? I suspect that $140 was chosen because it is 50% of $280, and most margin calculation start at 50% margin borrowing. So it makes intuitive sense, but maybe not really that applicable to terms of math. Maybe we could find some other option which has the same market exposure and narrower bid/ask spreads?
OK, Suppose I want to own 100 shares of SPY in 2 years. You own 100 shares of SPY right now. SPY is right now selling at i dollares. I pay you p dollars for the right to buy your shares two years from now at a strike of s deep in the money say. Well, you know that with enormous probability your shares are going to get called away in two years at the strike. So basically you are in the position of loaning me, i - p dollars for two years. It's almost without risk (unless the index goes below the strike). So, you want to get a fair loan value for your money. The dividends being thrown off in that 2 year period are a significant portion of you obtaining the fair loan value for your money. The S&P 500 throws off like 2% in dividend yield. The 1 year Libor is like 2.9%. So, basically, if you look at the calculation I did above, the dividend on the whole 100 shares is the interest paid to you for carrying this loan.

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Re: On Leverage

Post by pezblanco » Fri Mar 15, 2019 2:53 pm

DonIce wrote:
Fri Mar 15, 2019 1:26 pm
Just use futures. Simpler and cheaper.
The main problem for small retail investors I think is the size of the contract. An e-mini 500 contract is 141K today. If you want a leverage of 1.5 say, then you need to come up with around 91K. So, as the market rises and falls, it's hard to reset your leverage unless you are already so wealthy that 100K is in the fine granularity of your portfolio decisions.

Basically the borrowing calculations I'm doing is for using deep in the money LEAPS as future contracts. Before buying an e-mini 500 contract, I would want to do the exact same calculation.

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Re: On Leverage

Post by DonIce » Fri Mar 15, 2019 3:48 pm

pezblanco wrote:
Fri Mar 15, 2019 2:53 pm
The main problem for small retail investors I think is the size of the contract. An e-mini 500 contract is 141K today. If you want a leverage of 1.5 say, then you need to come up with around 91K. So, as the market rises and falls, it's hard to reset your leverage unless you are already so wealthy that 100K is in the fine granularity of your portfolio decisions.
If you've got 91k in cash in your account as collateral for the 1.5x leverage on the future contract, you can put some of that cash into an ETF (or inverse ETF) to adjust your holding on a finer scale than adding/subtracting a whole futures contract.

If your portfolio is only 10-20k or something cause you're in the first few years of accumulation then you're probably not ready to use leverage yet anyway, since it takes a while to really learn about these things and a while in the markets to get a gauge of your risk tolerance.

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Re: On Leverage

Post by grayfox » Sun Mar 17, 2019 6:51 am

In previous episodes of On Leverage, we talked about what leveraging is and explored how to leverage your portfolio.
  • Using Traditional Leverage by borrowing with a margin account at places like Interactive Brokers.
  • Using Traditional Leverage by borrowing from a private party, e.g. family members.
  • Using Traditional Leverage by borrowing against other assets, like your house. (OK, really leveraging your house!)
  • Buying Leverage ETFs like UPRO (3x S&P500) and TMF (3x 20Y Treasury)
  • Buying deep-in-the-money long-dated call options, LEAPS. (Long-term Equity Antici Pation Securities)
NEXT: Why?

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Re: On Leverage

Post by acegolfer » Sun Mar 17, 2019 9:38 am

pezblanco wrote:
Fri Mar 15, 2019 2:53 pm
DonIce wrote:
Fri Mar 15, 2019 1:26 pm
Just use futures. Simpler and cheaper.
The main problem for small retail investors I think is the size of the contract. An e-mini 500 contract is 141K today. If you want a leverage of 1.5 say, then you need to come up with around 91K. So, as the market rises and falls, it's hard to reset your leverage unless you are already so wealthy that 100K is in the fine granularity of your portfolio decisions.

Basically the borrowing calculations I'm doing is for using deep in the money LEAPS as future contracts. Before buying an e-mini 500 contract, I would want to do the exact same calculation.
$141k is the amount you agree to pay in future. It's not how much you need to pay "today". How much you pay today depends on the "initial margin requirement". As of now, according to TD Ameritrade, the initial margin requirement for June 2019 emini 500 is $6,600 per contract. Then you are leveraged = 141k/6.6k = 21.36 times.

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Re: On Leverage

Post by pezblanco » Sun Mar 17, 2019 2:32 pm

acegolfer wrote:
Sun Mar 17, 2019 9:38 am
pezblanco wrote:
Fri Mar 15, 2019 2:53 pm
DonIce wrote:
Fri Mar 15, 2019 1:26 pm
Just use futures. Simpler and cheaper.
The main problem for small retail investors I think is the size of the contract. An e-mini 500 contract is 141K today. If you want a leverage of 1.5 say, then you need to come up with around 91K. So, as the market rises and falls, it's hard to reset your leverage unless you are already so wealthy that 100K is in the fine granularity of your portfolio decisions.

Basically the borrowing calculations I'm doing is for using deep in the money LEAPS as future contracts. Before buying an e-mini 500 contract, I would want to do the exact same calculation.
$141k is the amount you agree to pay in future. It's not how much you need to pay "today". How much you pay today depends on the "initial margin requirement". As of now, according to TD Ameritrade, the initial margin requirement for June 2019 emini 500 is $6,600 per contract. Then you are leveraged = 141k/6.6k = 21.36 times.
Yes. But in this thread, we've been considering setting "reasonable" amounts of leverage for long term buy/hold. So, the leverage values of interest are from 1 to 3 more or less .... The Kelly criterion would be telling us something in the range of 1.2 to 1.5 so 21.36 is way out of the orbit of what is being considered.

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Re: On Leverage

Post by grayfox » Mon Mar 18, 2019 8:05 am

OK, so I said I would talk about the why.

:?: Why use leverage? Obviously, because it's amplifies the return. That's always been true. But why is there so much interest in using leverage at this time? I have a theory.

Historically, in round numbers, stocks have returned 10% and bonds have return 5%, per year, before inflation. See Vanguard
After 3% inflation, stocks returned 7% and bonds 2%.
A 60/40 portfolio returned 5%, after inflation.
At 5%, $1,000 at age 25, would compound to $7,040 by age 65.
That worked out pretty good. That's 7x real spending increase.

Today 20-year bonds are yielding only 2.85%. After 2% expected inflation, 0.85%. (20-Year TIPS are also yielding 0.85%. Hence 2% inflation expectations.)
For U.S. stocks, CAPE = 30. This implies a real return of about 3.3%.
In round numbers, I'll call it 3.5% for stocks and 1% for bonds.
:arrow: Expected return of stocks and bonds are half of what they were historically. :!:

A 60/40 portfolio would return only 2.5%, after inflation.
At 2.5%, $1,000 at age 25, would compound to only $2,685 by age 65, way below the historical $7,040. :x

One solution is to save more. If you were saving 15% of take-home pay, you will have to multiply that by 2.6 to get the same result. (It's more than 2x because of compounding.) That would be a saving rate of 39%. :x
Another solution is to work longer. For $1,000 to get to the same $7,040 would take 79 years. So you would have to keep working until age 104. :x
You could also do a combination of saving more and working longer. But no matter how you slice it, you are worse off than historical.

The third solution is to hold a riskier portfolio that doubles the meager expected return of stocks and bonds.
One was is to tilt toward risker assets, like SCV or Emerging markets. I don't know if this can double the return over S&P500. So that probably won't work by itself.
Another way is to use leverage. Then you can multiple the return by a factor like 2x.

:idea: That's my theory. Expected Returns for stocks and bonds are half of what they have been historically. To get back to decent returns, a lot of investors are deciding that will have to take on greater risk and lever up the meager returns that are currently offered by the market.
Last edited by grayfox on Tue Mar 19, 2019 11:31 am, edited 1 time in total.

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Re: On Leverage

Post by grayfox » Tue Mar 19, 2019 9:56 am

So there is all this interest in leverage. My theory is that it is because of low expected returns. But now I notice on another thread that a longtime poster is exiting stocks and bonds for the same reason, i.e. low expected returns! They are to 0/0/100 stocks/bonds/cash.

The idea is, If you already have enough, why take on the risk of stocks or even LT bonds when they offer such paltry reward? Everyone must have some point where they think the risk is not worth it. That point is different from everyone, but if you already have enough to retire on zero real return it is logical to invest it risk free.

Meanwhile, back at the ranch, those who still have a long way to go to make their goal, they are looking at levering up the measly returns by 2x.

Both are logical responses to the high stock valuation, low interest rate, flat-yield curve world we are in.
Interesting development.

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Re: On Leverage

Post by acegolfer » Tue Mar 19, 2019 11:29 am

pezblanco wrote:
Sun Mar 17, 2019 2:32 pm
Yes. But in this thread, we've been considering setting "reasonable" amounts of leverage for long term buy/hold. So, the leverage values of interest are from 1 to 3 more or less .... The Kelly criterion would be telling us something in the range of 1.2 to 1.5 so 21.36 is way out of the orbit of what is being considered.
Leverage implies you need less investment to achieve the same $ return. Suppose you want to invest $1 mil. The same $ return can be achieved with $50k investment w/ 20x leverage ratio. What's out of orbit is investing all $1 mil in 20x leveraged investment.

If anyone doesn't know how leverage works, then I suggest one should not use leverage.

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Re: On Leverage

Post by acegolfer » Tue Mar 19, 2019 11:50 am

grayfox wrote:
Mon Mar 18, 2019 8:05 am
:idea: That's my theory. Expected Returns for stocks and bonds are half of what they have been historically. To get back to decent returns, a lot of investors are deciding that will have to take on greater risk and lever up the meager returns that are currently offered by the market.
Interesting theory. 2 comments:

1. Shouldn't you claim that expected return is half of "historical average" return? If yes, then people will need to use leverage to achieve the historical average returns.

2. Not only there's a demand for leveraged products but also we can offer more leveraged products with the help of development in financial derivatives.

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Re: On Leverage

Post by pezblanco » Tue Mar 19, 2019 2:35 pm

acegolfer wrote:
Tue Mar 19, 2019 11:29 am
pezblanco wrote:
Sun Mar 17, 2019 2:32 pm
Yes. But in this thread, we've been considering setting "reasonable" amounts of leverage for long term buy/hold. So, the leverage values of interest are from 1 to 3 more or less .... The Kelly criterion would be telling us something in the range of 1.2 to 1.5 so 21.36 is way out of the orbit of what is being considered.
Leverage implies you need less investment to achieve the same $ return. Suppose you want to invest $1 mil. The same $ return can be achieved with $50k investment w/ 20x leverage ratio. What's out of orbit is investing all $1 mil in 20x leveraged investment.
I don't understand why you wrote this ... it in no way is disagreeing with what you quoted.

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Re: On Leverage

Post by acegolfer » Tue Mar 19, 2019 2:56 pm

pezblanco wrote:
Tue Mar 19, 2019 2:35 pm
acegolfer wrote:
Tue Mar 19, 2019 11:29 am
pezblanco wrote:
Sun Mar 17, 2019 2:32 pm
Yes. But in this thread, we've been considering setting "reasonable" amounts of leverage for long term buy/hold. So, the leverage values of interest are from 1 to 3 more or less .... The Kelly criterion would be telling us something in the range of 1.2 to 1.5 so 21.36 is way out of the orbit of what is being considered.
Leverage implies you need less investment to achieve the same $ return. Suppose you want to invest $1 mil. The same $ return can be achieved with $50k investment w/ 20x leverage ratio. What's out of orbit is investing all $1 mil in 20x leveraged investment.
I don't understand why you wrote this ... it in no way is disagreeing with what you quoted.
My bad. I thought you disagreed with Donice who said futures is simpler and cheaper. I was making an argument for Donice.

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Re: On Leverage

Post by inbox788 » Tue Mar 19, 2019 3:33 pm

acegolfer wrote:
Tue Mar 19, 2019 11:50 am
1. Shouldn't you claim that expected return is half of "historical average" return? If yes, then people will need to use leverage to achieve the historical average returns.

2. Not only there's a demand for leveraged products but also we can offer more leveraged products with the help of development in financial derivatives.
Leverage isn't magically doubling return; it's taking return from elsewhere. Who are the losers in leverage when someone takes twice their share of pie? If this leverage strategy does work out and a lot of people adopt it, it will expose where their taking from, and I only see 2 places:

1) small pieces from all of us, which mean less than historical average returns
2) big pieces from active players, who will get no return or negative return

I think it's more of the latter, and how do you know that your strategy isn't the active participant giving up your share or more?

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Re: On Leverage

Post by BJJ_GUY » Tue Mar 19, 2019 3:45 pm

acegolfer wrote:
Tue Mar 19, 2019 11:50 am
grayfox wrote:
Mon Mar 18, 2019 8:05 am
:idea: That's my theory. Expected Returns for stocks and bonds are half of what they have been historically. To get back to decent returns, a lot of investors are deciding that will have to take on greater risk and lever up the meager returns that are currently offered by the market.
Interesting theory. 2 comments:

1. Shouldn't you claim that expected return is half of "historical average" return? If yes, then people will need to use leverage to achieve the historical average returns.

2. Not only there's a demand for leveraged products but also we can offer more leveraged products with the help of development in financial derivatives.
Careful with the math here. Expected returns are generally expressed as an arithmetic average (needing the mean when thinking about variance in a distribution construct).

The difference between the arithmetic and geometric returns are entirely explained by the variance in returns that are actually experienced.

When using leverage to gain exposure above 100% nominal market value, the volatility drag is more pronounced.

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Re: On Leverage

Post by grayfox » Sat Mar 23, 2019 7:15 am

When yield curve inverts, how do these leverage strategies perform? For instance, about Feb-2006, the yield curve first started inverting. Does anyone have any simulations showing what would have happened starting around the beginning of 2006.

Here is 200/-100 VFINX/CASHX and leveraged ETF SSO (2xS&P500) from Feb-2006 to Feb-2019 on portviz. portviz

Code: Select all

	Initial	Final	CAGR	Stdev	Best	Worst	Max. DD	Sharpe	Sortino	US Mkt Correlation
2xVFINX	$10,000	$36,088 10.66% 	31.59%	64.35%	-75.17%	-85.70% 0.46	0.63	0.98
SSO	$10,000	$36,745 10.82%	29.45%	70.46%	-67.94%	-81.35% 0.47	0.67	0.99
Only -81% drawdown. Sign me up! :D


How about the 3x 40/60 strategy using leveraged ETFs?

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Re: On Leverage

Post by grayfox » Sun Mar 24, 2019 6:49 am

No responce. OK, I will run portwiz on 120/180/-200 VFINX/VUSTX/CASHX from Feb-2006 to Dec-2010.
I compared it to 100% S&P500 and 60/40 portfolio. Link

Surprisingly, it looks like 3x40/60 practically sailed right through the 2008/2009 debacle :!: At least compared to 100% S&P500
It did get down to 7,163 in Feb-2009 but that is better than VFINX which was down to 6,119

Code: Select all

	Initial	Final	CAGR	Stdev	Best	Worst	Max. DD	Sharpe	Sortino	US Mkt Correlation
3x40/60	$10,000	$17,189 11.65% 	32.19%	33.76%	-7.11%	-44.23% 0.44	0.68	0.55
VFINX	$10,000	$10,869 1.71% 	17.94%	26.49%	-37.02%	-50.97% 0.06	0.08	1.00
60/40	$10,000	$12,604 4.82% 	10.85%	12.52%	-13.21%	-26.96% 0.29	0.39	0.87
Max DD was -44.23% which is not as bad as VFINX -50.97%

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Re: On Leverage

Post by HEDGEFUNDIE » Sun Mar 24, 2019 8:24 am

grayfox wrote:
Sun Mar 24, 2019 6:49 am
No responce. OK, I will run portwiz on 120/180/-200 VFINX/VUSTX/CASHX from Feb-2006 to Dec-2010.
I compared it to 100% S&P500 and 60/40 portfolio. Link

Surprisingly, it looks like 3x40/60 practically sailed right through the 2008/2009 debacle :!: At least compared to 100% S&P500
It did get down to 7,163 in Feb-2009 but that is better than VFINX which was down to 6,119

Code: Select all

	Initial	Final	CAGR	Stdev	Best	Worst	Max. DD	Sharpe	Sortino	US Mkt Correlation
3x40/60	$10,000	$17,189 11.65% 	32.19%	33.76%	-7.11%	-44.23% 0.44	0.68	0.55
VFINX	$10,000	$10,869 1.71% 	17.94%	26.49%	-37.02%	-50.97% 0.06	0.08	1.00
60/40	$10,000	$12,604 4.82% 	10.85%	12.52%	-13.21%	-26.96% 0.29	0.39	0.87
Max DD was -44.23% which is not as bad as VFINX -50.97%
Why is this a surprise? It is the entire basis of my 28 page thread.

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