## On Leverage

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
Topic Author
grayfox
Posts: 5046
Joined: Sat Sep 15, 2007 4:30 am

### On Leverage

I have been seeing a lot of posts about using leverage so I thought that I would look into it. I've never bought stocks on margin or used leverage in investing, so this will be very basic. Advanced investors can skip it.

My understanding is if you have an investment like a stock that is expected to produce a positive return, you can buy some with your own money, and buy some more with borrowed money. At the end, you sell the stock, payoff the loan plus interest with the proceeds, and you made more profit than if you didn't use levarage.

I'll do a simple example. Let's say you have \$1,000. With no leverage, you buy \$1,000 worth of stock and hold it for one year. Of course, stocks can go up or down. For simplicity, let's say there's a 0.90 probability that the stock will return +10% and a 0.10 probability that it will return -10%.
If it goes up, you have \$1,100 but if it goes down you have \$900. Expected Return** = 8.00%

With 2x leverage, you borrow \$1,000 and can buy \$2,000 total worth of stock. Let's say the interest rate is 5% p.a. Same outcome probabilites.
If it goes up +10%, NAV = \$2,200. Sell, payoff the \$1,000 loan + \$50 interest and you take out \$1,150. Return = +15%
If it goes down -10%, NAV = \$1,800. Sell, payoff the \$1,000 loan + \$50 interest and you take out \$750. Return = -25%
Expected Return = 11.00%

So with 2x leverage and 5% interest rate, the distribution of possible outcomes changed from -10% / +10% into -25% / +15%
Expected Return increased from 8.00% to 11.00% (2x minus 5% that you have to pay in interest.)

With leverage, the probability distribution of outcomes shifts to the right and gets wider. In other words, greater reward (expected return) comes with greater risk (variance). No free lunch here.

** Expected Return = probability-weighted sum of all the outcomes

AHTFY
Posts: 29
Joined: Mon Jul 23, 2018 2:33 pm

### Re: On Leverage

grayfox wrote:
Fri Feb 15, 2019 8:50 am
So with 2x leverage and 5% interest rate, the distribution of possible outcomes changed from -10% / +10% into -25% / +15%
Expected Return increased from 8.00% to 11.00% (2x minus 5% that you have to pay in interest.)
So to simplify, your risk-adjusted return (your return above the risk-free rate) goes from 3% to 6% with 2x leverage, exactly what you'd expect.

Of course you are ignoring your risk of ruin (chance you lose 100%), which goes from 0% to some higher number because the market occasionally does fall 50%.

305pelusa
Posts: 181
Joined: Fri Nov 16, 2018 10:20 pm

### Re: On Leverage

You have computed the expected (aka average) return. But you're not taking into account that what matters is compounded returns. And volatility drag will decrease that. Here's how to go from expected to compounded:

Unleveraged:
You invest 1k which grows 10% for 9 years and then drops 10% on the tenth year. That's 1000*1.1^(9)*0.9=2122. That's what you have after ten years. So the compound rate is 1000*x^(10) = 2122. Solve for x and you get 7.8%. No surprises here. We know compound returns will always be a little lower than expected/average due to volatility drag.

Also note the sequence of years does not matter. First year could be bad then 9 good ones. Multiplication doesn't care for the order here because we're not taking the money out during that time.

Leveraged:
You put 1000 and get a 1000 loan. Let's just say they let you defer all loan payments til the end for moment. Using the same math above 2000*1.1^(9)*0.9 = 4244. Sell, pay 1000 loan and 500 in interests, you end with 2744.

We find compound interest as 1000*x^10= 2744. It's 10.6%. Note how little the compound interest dropped from average in the unleveraged case, and how it dropped from average in leveraged.

But that's not all.
You don't get to defer loan payments. You pay them yearly. Now sequence of events matter. Best case, the first 9 good years come first then a bad one. That decreases your final amount to 2583, for a compound return of 9.96%.

Worst case scenario, bad year is the first year. Now the final amount is 2447 for a compound return of 9.36%. The worst case and best case are equally likely so let's just call it a nominal 9.66% if you don't get to defer loan payments. Which you don't.

Note how much more the compound returns of the leveraged case drop below the expected when compared to the unleveraged case. It's no longer 8vs11%. It's 7.8vs9.66%.

And the more volatile the asset, the bigger the effect. The standard deviation of your example is a measly 6.3 but stocks have more like 15%.
And the further leveraged you are, the bigger that effect as well. In both cases you take increasingly bigger risk for significantly less returns.

I'm convinced it's a loser's game and succeeds only if you can speculate properly. I'm certainly open to someone changing my mind though.

aristotelian
Posts: 5368
Joined: Wed Jan 11, 2017 8:05 pm

### Re: On Leverage

305pelusa wrote:
Fri Feb 15, 2019 9:45 am

I'm convinced it's a loser's game and succeeds only if you can speculate properly. I'm certainly open to someone changing my mind though.
Did you never carry a mortgage and invest at the same time?

Topic Author
grayfox
Posts: 5046
Joined: Sat Sep 15, 2007 4:30 am

### Re: On Leverage

AHTFY wrote:
Fri Feb 15, 2019 9:25 am

Of course you are ignoring your risk of ruin (chance you lose 100%), which goes from 0% to some higher number because the market occasionally does fall 50%.
Right. I'll do a slightly more realistic example. I found the annual return of S&P500 1928-2015 here https://seekingalpha.com/instablog/6052 ... -1928-2015 The worst year was 1991 -43.84% and the best year was 1954 +52.56. I think the median was in the neighborhood of +10%.

That is sure a wide range of possible outcomes over one year. I'm going to round the worst case to -50%, like you suggested, and the best case to +60% and pretend that this is the distribution of possible outcomes.

Outcome Probability
-50% 0.05 worst
+10% 0.90 median
+60% 0.05 best

Again I put in \$1,000. With no leverage, my median outcome is I gain +10% and take home \$1,100.
My best case is I gain +60% and take home \$1,600
My worst case is -50% loss and I take home \$500.
E.R. = 9.50%

With 2x leverage and 5% cost of borrowing, my median case is +15% gain and I take home \$1,150.
My best case is I gain +115% and take home \$2,150. Sweet!
My worst case is -105% loss and I take home -\$50. I lost my \$1,000 plus I owe the bank \$50.
E.R. = 14.00%%

As before, both the Expected Return and variance increased. The distribution extended to the right, which is good. But it also extended to the left, which is bad. In fact, so far to the left that the worst case was beyond -100%, more than a total loss. Ruin!

My takeaway is that you should consider the whole probability distribution of outcomes for the underlying investment. Not just the median, or the mean, but all the possibilities, especially the worst case. And then determine how leverage changes the outcome distribution, i.e. widens it (variance) and shifts the center (median or mean).

Topic Author
grayfox
Posts: 5046
Joined: Sat Sep 15, 2007 4:30 am

### Re: On Leverage

aristotelian wrote:
Fri Feb 15, 2019 9:49 am
305pelusa wrote:
Fri Feb 15, 2019 9:45 am

I'm convinced it's a loser's game and succeeds only if you can speculate properly. I'm certainly open to someone changing my mind though.
Did you never carry a mortgage and invest at the same time?
That is another good thought.

Seeing that 2x leverage will go bust when the market drops by -50%, and knowing that it happened in the past, that would mean that you definitely don't want to leverage with a callable loan. That rules out buying stocks on margin by borrowing from a broker. You will be forced to sell your stock when it is down, the worst time sell. That is definitely the road to ruin.

But, as you suggest, if you borrow against your house, I'm pretty sure that is non-callable. That might be something to consider.

My takeaway here is do not get leverage with a callable loan. You never want to be forced to sell.

305pelusa
Posts: 181
Joined: Fri Nov 16, 2018 10:20 pm

### Re: On Leverage

aristotelian wrote:
Fri Feb 15, 2019 9:49 am
305pelusa wrote:
Fri Feb 15, 2019 9:45 am

I'm convinced it's a loser's game and succeeds only if you can speculate properly. I'm certainly open to someone changing my mind though.
Did you never carry a mortgage and invest at the same time?
I will admit I have not (haven't bought a house). But when it comes to that, I'll certainly take a hard look at the numbers (mortgage rate, expected stock returns and their volatility, etc). My assumption is that mortgage rates are generally lower than margin rates. That significantly changes the above math in favor of leverage.

So I will concede it depends on specifics so perhaps it's a good choice all things considered. My post was merely to point out that what matters is compounded, not average returns. And that leverage, due to increased volatility drag, will lower that compound return by more than the unleveraged case.

alex_686
Posts: 4421
Joined: Mon Feb 09, 2015 2:39 pm

### Re: On Leverage

305pelusa wrote:
Fri Feb 15, 2019 10:27 am
I will admit I have not (haven't bought a house). But when it comes to that, I'll certainly take a hard look at the numbers (mortgage rate, expected stock returns and their volatility, etc). My assumption is that mortgage rates are generally lower than margin rates. That significantly changes the above math in favor of leverage.

So I will concede it depends on specifics so perhaps it's a good choice all things considered. My post was merely to point out that what matters is compounded, not average returns. And that leverage, due to increased volatility drag, will lower that compound return by more than the unleveraged case.
Generally speaking, pairing a low volatility asset like a houses and rental property with a mortgage is a good deal. There are exceptions - see 2008.

So, I worked the margin desk during the dot.com boom and bust, and you are partially right about leverage and volatility drag - but you can't make that argument with certainty. There has been heavy discussion on this board and in the literature on this subject. As a counterpoint, there is a strong argument to be had that Warren Buffet's success was buying companies with the "quality" and "low volatility" factors, and then leveraging them up via the insurance portfolio. In this case, the leveraged low volatility stocks had a lower volatility drag then the market as a whole.

305pelusa
Posts: 181
Joined: Fri Nov 16, 2018 10:20 pm

### Re: On Leverage

grayfox wrote:
Fri Feb 15, 2019 9:56 am
AHTFY wrote:
Fri Feb 15, 2019 9:25 am

Of course you are ignoring your risk of ruin (chance you lose 100%), which goes from 0% to some higher number because the market occasionally does fall 50%.
Right. I'll do a slightly more realistic example. I found the annual return of S&P500 1928-2015 here https://seekingalpha.com/instablog/6052 ... -1928-2015 The worst year was 1991 -43.84% and the best year was 1954 +52.56. I think the median was in the neighborhood of +10%.

That is sure a wide range of possible outcomes over one year. I'm going to round the worst case to -50%, like you suggested, and the best case to +60% and pretend that this is the distribution of possible outcomes.

Outcome Probability
-50% 0.05 worst
+10% 0.90 median
+60% 0.05 best

Again I put in \$1,000. With no leverage, my median outcome is I gain +10% and take home \$1,100.
My best case is I gain +60% and take home \$1,600
My worst case is -50% loss and I take home \$500.
E.R. = 9.50%

With 2x leverage and 5% cost of borrowing, my median case is +15% gain and I take home \$1,150.
My best case is I gain +115% and take home \$2,150. Sweet!
My worst case is -105% loss and I take home -\$50. I lost my \$1,000 plus I owe the bank \$50.
E.R. = 14.00%%

As before, both the Expected Return and variance increased. The distribution extended to the right, which is good. But it also extended to the left, which is bad. In fact, so far to the left that the worst case was beyond -100%, more than a total loss. Ruin!

My takeaway is that you should consider the whole probability distribution of outcomes for the underlying investment. Not just the median, or the mean, but all the possibilities, especially the worst case. And then determine how leverage changes the outcome distribution, i.e. widens it (variance) and shifts the center (median or mean).
EDIT : Checked my math and updated numbers.
For your new example, If you compute the compound return of the unleveraged, you get 7.75%. The leveraged is 9.15%. People should check my math of course

Again, compound (CAGR) is what matters. And the more volatile (your numbers have a St. Dev of 18.4 this time, so much more representative), the larger this volatility drag.

Btw, this website calculates the average and compounded return of the S and P 500 for any time period. For your time period, it was 12% average and 10% compounded. You were a bit off from your estimations:
http://www.moneychimp.com/features/market_cagr.htm

It also talks a bit about the difference between the expected and the compounded (aka annualized).

305pelusa
Posts: 181
Joined: Fri Nov 16, 2018 10:20 pm

### Re: On Leverage

BTW OP I apologize if I sound pedantic. It's a great thread and I'm glad you opened. I just wanted to offer that brief viewpoint. I take away what you did as well. I'm not sure there's a free lunch here. There are better returns and higher risks

aristotelian
Posts: 5368
Joined: Wed Jan 11, 2017 8:05 pm

### Re: On Leverage

grayfox wrote:
Fri Feb 15, 2019 10:11 am
aristotelian wrote:
Fri Feb 15, 2019 9:49 am
Did you never carry a mortgage and invest at the same time?
That is another good thought.

Seeing that 2x leverage will go bust when the market drops by -50%, and knowing that it happened in the past, that would mean that you definitely don't want to leverage with a callable loan. That rules out buying stocks on margin by borrowing from a broker. You will be forced to sell your stock when it is down, the worst time sell. That is definitely the road to ruin.

But, as you suggest, if you borrow against your house, I'm pretty sure that is non-callable. That might be something to consider.

My takeaway here is do not get leverage with a callable loan. You never want to be forced to sell.
Yes, the timeframe of the loan matters, too. With a 30 year mortgage, you have a much better chance at coming out ahead than a margin loan or credit card balance transfer.

2015
Posts: 2855
Joined: Mon Feb 10, 2014 2:32 pm

### Re: On Leverage

grayfox wrote:
Fri Feb 15, 2019 8:50 am
I have been seeing a lot of posts about using leverage so I thought that I would look into it. I've never bought stocks on margin or used leverage in investing, so this will be very basic. Advanced investors can skip it.

...
With all due respect, grayfox, what are you looking for? Positive feedback on yet another gambling scheme here? Historically, leverage of any kind has been one of the fastest roads to ruin for many an investor (most recently, 2008 housing crisis). IMO, there are no "advanced investors", only those drenched in overconfidence playing a mug's game in the fun house ride of unpredictable complex adaptive systems. It's like any gold rush, a few win, then the fools rush in. Amateurs play to win (which is why they're always losing), while professionals play not to lose. An amateur always thinks they're a professional while a professional never makes that mistake.

HEDGEFUNDIE
Posts: 2077
Joined: Sun Oct 22, 2017 2:06 pm

### Re: On Leverage

2015 wrote:
Fri Feb 15, 2019 12:55 pm
grayfox wrote:
Fri Feb 15, 2019 8:50 am
I have been seeing a lot of posts about using leverage so I thought that I would look into it. I've never bought stocks on margin or used leverage in investing, so this will be very basic. Advanced investors can skip it.

...
With all due respect, grayfox, what are you looking for? Positive feedback on yet another gambling scheme here? Historically, leverage of any kind has been one of the fastest roads to ruin for many an investor (most recently, 2008 housing crisis). IMO, there are no "advanced investors", only those drenched in overconfidence playing a mug's game in the fun house ride of unpredictable complex adaptive systems. It's like any gold rush, a few win, then the fools rush in. Amateurs play to win (which is why they're always losing), while professionals play not to lose. An amateur always thinks they're a professional while a professional never makes that mistake.
The free lunch is what it has always been: Diversification.

In this case, diversification along the assets you hold and diversification of the timeframe (i.e. economic conditions) in which you hold them.

So the longer the timeframe you have in front of you, and the more diversified your asset base, the more leverage makes sense.

ThrustVectoring
Posts: 654
Joined: Wed Jul 12, 2017 2:51 pm

### Re: On Leverage

Don't touch leverage without a good understanding of risk of ruin, volatility drag, Kelly Criterion, and general risk management strategies. The counter-parties you interact with are willing to give you more leverage than you should use.

Kelly Criterion, in short: as asset prices change, you need to buy and sell in order to maintain the correct amount of leverage. The higher the leverage, the more you have to buy when prices go up and sell when prices go down. This adds a drag on returns over and above the direct cost of leverage, and with volatile enough assets you're better off keeping "dry powder" for future investment opportunities. This effect is counterbalanced by the fact that risky investment yields more, and the Kelly Criterion is how you find the balancing point where more leverage starts hurting your expected returns. Last time I ran the numbers given expected volatility and returns, it came out to something like 140% stock exposure. Kelly portfolios have really wide dispersion of results, so partial-Kelly is usually recommended in practice, so that all was enough to get me to consider and then reject leverage as a permanent part of my portfolio.

Time diversification makes some sense, especially because it means that you aren't robotically doing rebalances to maintain a specific percentage allocation to a risky asset. Especially with a non-callable source of funding - it means you can target a specific amount of risk to take, and whatever portfolio value and leverage that entails is fine so long as your income is secure enough to service the debt payments.
Current portfolio: 60% VTI / 40% VXUS

305pelusa
Posts: 181
Joined: Fri Nov 16, 2018 10:20 pm

### Re: On Leverage

HEDGEFUNDIE wrote:
Fri Feb 15, 2019 2:33 pm
2015 wrote:
Fri Feb 15, 2019 12:55 pm
grayfox wrote:
Fri Feb 15, 2019 8:50 am
I have been seeing a lot of posts about using leverage so I thought that I would look into it. I've never bought stocks on margin or used leverage in investing, so this will be very basic. Advanced investors can skip it.

...
With all due respect, grayfox, what are you looking for? Positive feedback on yet another gambling scheme here? Historically, leverage of any kind has been one of the fastest roads to ruin for many an investor (most recently, 2008 housing crisis). IMO, there are no "advanced investors", only those drenched in overconfidence playing a mug's game in the fun house ride of unpredictable complex adaptive systems. It's like any gold rush, a few win, then the fools rush in. Amateurs play to win (which is why they're always losing), while professionals play not to lose. An amateur always thinks they're a professional while a professional never makes that mistake.
The free lunch is what it has always been: Diversification.

In this case, diversification along the assets you hold and diversification of the timeframe (i.e. economic conditions) in which you hold them.

So the longer the timeframe you have in front of you, and the more diversified your asset base, the more leverage makes sense.
That makes sense because all diversification truly does is lower volatility. That means less volatility drag.

I don't have a good intuition for what it takes but just doing some back of the envelope stuff, I think you basically need things that are negatively correlated. Probably strongly so. If you believe you've found that, then leveraging it would make sense in my mind.

Interestingly, this might answer to an extent why mortgaging and using any extra money on stocks could make sense. As long as the house price/imputed rent isn't particularly correlated with stocks, then it's not as bad as the situations I've pointed out earlier

But simply leveraging X asset without something that specifically grows when that one shrinks? The volatility drag, yearly loan interest and sequence of events can take some giant bites to the returns.

HEDGEFUNDIE
Posts: 2077
Joined: Sun Oct 22, 2017 2:06 pm

### Re: On Leverage

305pelusa wrote:
Fri Feb 15, 2019 5:12 pm
HEDGEFUNDIE wrote:
Fri Feb 15, 2019 2:33 pm
2015 wrote:
Fri Feb 15, 2019 12:55 pm
grayfox wrote:
Fri Feb 15, 2019 8:50 am
I have been seeing a lot of posts about using leverage so I thought that I would look into it. I've never bought stocks on margin or used leverage in investing, so this will be very basic. Advanced investors can skip it.

...
With all due respect, grayfox, what are you looking for? Positive feedback on yet another gambling scheme here? Historically, leverage of any kind has been one of the fastest roads to ruin for many an investor (most recently, 2008 housing crisis). IMO, there are no "advanced investors", only those drenched in overconfidence playing a mug's game in the fun house ride of unpredictable complex adaptive systems. It's like any gold rush, a few win, then the fools rush in. Amateurs play to win (which is why they're always losing), while professionals play not to lose. An amateur always thinks they're a professional while a professional never makes that mistake.
The free lunch is what it has always been: Diversification.

In this case, diversification along the assets you hold and diversification of the timeframe (i.e. economic conditions) in which you hold them.

So the longer the timeframe you have in front of you, and the more diversified your asset base, the more leverage makes sense.
That makes sense because all diversification truly does is lower volatility. That means less volatility drag.

I don't have a good intuition for what it takes but just doing some back of the envelope stuff, I think you basically need things that are negatively correlated. Probably strongly so. If you believe you've found that, then leveraging it would make sense in my mind.

Interestingly, this might answer to an extent why mortgaging and using any extra money on stocks could make sense. As long as the house price/imputed rent isn't particularly correlated with stocks, then it's not as bad as the situations I've pointed out earlier

But simply leveraging X asset without something that specifically grows when that one shrinks? The volatility drag, yearly loan interest and sequence of events can take some giant bites to the returns.
Agree 100% with all of this.

longinvest
Posts: 3288
Joined: Sat Aug 11, 2012 8:44 am

### Re: On Leverage

aristotelian wrote:
Fri Feb 15, 2019 9:49 am
Did you never carry a mortgage and invest at the same time?
This is a framing mistake. The mortgage leverages the real estate investment (the house), not the portfolio.

dknightd
Posts: 1365
Joined: Wed Mar 07, 2018 11:57 am

### Re: On Leverage

longinvest wrote:
Fri Feb 15, 2019 5:37 pm
aristotelian wrote:
Fri Feb 15, 2019 9:49 am
Did you never carry a mortgage and invest at the same time?
This is a framing mistake. The mortgage leverages the real estate investment (the house), not the portfolio.
I would not take out a loan on my house to invest in the stock market.
On the other hand, instead of investing, I could pay off the home loan. But in the long term I'm pretty sure that would be a mistake.

It could be a "framing mistake", or it could be called "mental accounting". I'm leveraging my house, but not my retirement investments. If you put them together, then in effect I am leveraging my investments.

The interesting thing is that buying a house, and investing for retirement, and living in retirement, all have the same basic timeline (about 30 years)

My mental accounting says; I bought a house because I could not easily rent in the area I live. I could not afford to pay cash, so I took out a mortgage. I'm leveraging the place I live in, but the payments are known for the next 30 years. And it provides me with a place to live. I'm not looking at my home as an investment, I'm looking at it as a place to live with known loan repayment terms. (yes repairs and taxes are unknown)

I think most people who use leverage for investing are considering much shorter terms. Not 30 years. More like a day, or week, or month or two. They pay lower interest rates. In fact they may pay no interest at all (by selling stuff they do not own to raise funds), then "investing" the proceeds into something else. They are essentially "gambling" they are smarter than other people doing similar things. As the OP says, you can make money doing this. Or you can loose a bunch of money. I put "gambling" in quotes since the cost of doing this is probably much lower than the cost the gambling "house" needs to make. I suspect, but do not know, the costs for playing the market are less than playing black jack.

Anyway. I do not worry myself about these things. I'm in for the long haul. Buy a house on "leverage" if needed. Invest for retirement, not quick gains. Combine the above to live for 30+ more years with no income to bail me out.

305pelusa
Posts: 181
Joined: Fri Nov 16, 2018 10:20 pm

### Re: On Leverage

dknightd wrote:
Fri Feb 15, 2019 6:20 pm
longinvest wrote:
Fri Feb 15, 2019 5:37 pm
aristotelian wrote:
Fri Feb 15, 2019 9:49 am
Did you never carry a mortgage and invest at the same time?
This is a framing mistake. The mortgage leverages the real estate investment (the house), not the portfolio.
It could be a "framing mistake", or it could be called "mental accounting". I'm leveraging my house, but not my retirement investments. If you put them together, then in effect I am leveraging my investments.
No mental accounting; I agree with the previous poster. It is a framing issue.

Imagine you're given a loan. If you invest that money in purely one asset (stocks) I think you run into serious volatility drag. That's purely leverage.

Now imagine with that loan, you purely invest in Real Estate (aka your house). That would be akin to paying off the mortgage as fast as possible. This Isn't too bad because the imputed rent (rent you save from having your own home) has almost no volatility. You have to pay it one way or another. So those "returns" you get from not paying rent are fairly consistent. Little volatility drag.

If you invested in both (aka make mortgage payments AND invest in stocks on the side), then as long as they're somewhat uncorrelated (and they will be because your imputed rent is constant) then this is looking like a sound position to me. This is a similar concept to diversification.

The mortgage forces you to make mortgage payments, which forces you to invest to an extent in something other than stocks with your loan/leveraged positions (diversification). This is why I don't think it's as bad/why it's really a different scenario.. That feels like a consistent conclusion to me

longinvest
Posts: 3288
Joined: Sat Aug 11, 2012 8:44 am

### Re: On Leverage

dknightd wrote:
Fri Feb 15, 2019 6:20 pm
I'm leveraging my house, but not my retirement investments. If you put them together, then in effect I am leveraging my investments.
I disagree.

We used to own a condo. We had paid off the mortgage within a few years of buying it.

A few years ago we finally realized that owning wasn't our thing. Everybody had always told us that owning was the right financial decision, but we had reached the point where we didn't mind if renting was more expensive or not. We wanted out of real estate ownership.

We sold. Our portfolio immediately grew as if we had remained owners and had taken a new mortgage on the condo.

So, here's my question: is our bigger portfolio leveraged?

If not, why would have it been leveraged if we had remained owners and taken a mortgage equal to the value of the condo minus real estate agent commission? In both cases, the portfolio's starting value would be identical, and the return on it identical too.

The reality is that the portfolio isn't leveraged in either case.

Whether selling and renting or remortgaging wins will be fully determined by the outcome of the real estate investment relative to the cost of renting. The investment portfolio has nothing to do with the better or worse financial outcome.

As I said, the mortgage leverages the real estate investment.

AlohaJoe
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Location: Saigon, Vietnam

### Re: On Leverage

grayfox wrote:
Fri Feb 15, 2019 10:11 am
Seeing that 2x leverage will go bust when the market drops by -50%, and knowing that it happened in the past, that would mean that you definitely don't want to leverage with a callable loan. That rules out buying stocks on margin by borrowing from a broker. You will be forced to sell your stock when it is down, the worst time sell. That is definitely the road to ruin.
Or...you could leverage less than 2x.

dknightd
Posts: 1365
Joined: Wed Mar 07, 2018 11:57 am

### Re: On Leverage

305pelusa wrote:
Fri Feb 15, 2019 6:31 pm
dknightd wrote:
Fri Feb 15, 2019 6:20 pm
longinvest wrote:
Fri Feb 15, 2019 5:37 pm
aristotelian wrote:
Fri Feb 15, 2019 9:49 am
Did you never carry a mortgage and invest at the same time?
This is a framing mistake. The mortgage leverages the real estate investment (the house), not the portfolio.
It could be a "framing mistake", or it could be called "mental accounting". I'm leveraging my house, but not my retirement investments. If you put them together, then in effect I am leveraging my investments.
No mental accounting; I agree with the previous poster. It is a framing issue.

Imagine you're given a loan. If you invest that money in purely one asset (stocks) I think you run into serious volatility drag. That's purely leverage.

Now imagine with that loan, you purely invest in Real Estate (aka your house). That would be akin to paying off the mortgage as fast as possible. This Isn't too bad because the imputed rent (rent you save from having your own home) has almost no volatility. You have to pay it one way or another. So those "returns" you get from not paying rent are fairly consistent. Little volatility drag.

If you invested in both (aka make mortgage payments AND invest in stocks on the side), then as long as they're somewhat uncorrelated (and they will be because your imputed rent is constant) then this is looking like a sound position to me. This is a similar concept to diversification.

The mortgage forces you to make mortgage payments, which forces you to invest to an extent in something other than stocks with your loan/leveraged positions (diversification). This is why I don't think it's as bad/why it's really a different scenario.. That feels like a consistent conclusion to me
I''m not sure I understand the difference between "mental accounting" and a "framing issue."

I agree with the concept of diversified, uncorrelated expenses/income.
I'm not forced to keep paying my mortgage. I could sell the house and start renting. Something I might do one day.

AlohaJoe
Posts: 4260
Joined: Mon Nov 26, 2007 2:00 pm
Location: Saigon, Vietnam

### Re: On Leverage

305pelusa wrote:
Fri Feb 15, 2019 6:31 pm
Imagine you're given a loan. If you invest that money in purely one asset (stocks) I think you run into serious volatility drag. That's purely leverage.
Imagine I am 100% stocks. Then I take out a \$200,000 margin loan from my broker. That leaves me at 120% stocks and -20% cash. Then I use that cash to pay for an extravagant vacation.

Am I really not leveraged? Even though my broker and the SEC consider me leveraged?

Or are you saying that the source of collateral for a loan is what determines whether you have a leveraged portfolio?

dknightd
Posts: 1365
Joined: Wed Mar 07, 2018 11:57 am

### Re: On Leverage

longinvest wrote:
Fri Feb 15, 2019 6:44 pm
dknightd wrote:
Fri Feb 15, 2019 6:20 pm
I'm leveraging my house, but not my retirement investments. If you put them together, then in effect I am leveraging my investments.
I disagree.

We used to own a condo. We had paid off the mortgage within a few years of buying it.

A few years ago we finally realized that owning wasn't our thing. Everybody had always told us that owning was the right financial decision, but we had reached the point where we didn't mind if renting was more expensive or not. We wanted out of real estate ownership.

We sold. Our portfolio immediately grew as if we had remained owners and had taken a new mortgage on the condo.

So, here's my question: is our bigger portfolio leveraged?

If not, why would have it been leveraged if we had remained owners and taken a mortgage equal to the value of the condo minus real estate agent commission? In both cases, the portfolio's starting value would be identical, and the return on it identical too.

The reality is that the portfolio isn't leveraged in either case.

Whether selling and renting or remortgaging wins will be fully determined by the outcome of the real estate investment relative to the cost of renting. The investment portfolio has nothing to do with the better or worse financial outcome.

As I said, the mortgage leverages the real estate investment.
Agreed. But you sold off one investment (condo) and used the money someplace else. I still owe money on my house, which means I'm leveraged. Am I missing something?
If you had taken out a loan on your previously fully paid off condo, I think you would be leveraged. i.e. You are borrowing money against one asset to buy another asset.

As near as I can tell you decided that "realized that owning wasn't our thing". So you essentially moved one asset to another.

Now you have more money in the bank, but are renting a place to live. (something we might do when we want to move around)

I must be missing something?
Last edited by dknightd on Fri Feb 15, 2019 8:13 pm, edited 1 time in total.

HEDGEFUNDIE
Posts: 2077
Joined: Sun Oct 22, 2017 2:06 pm

### Re: On Leverage

AlohaJoe wrote:
Fri Feb 15, 2019 7:37 pm
grayfox wrote:
Fri Feb 15, 2019 10:11 am
Seeing that 2x leverage will go bust when the market drops by -50%, and knowing that it happened in the past, that would mean that you definitely don't want to leverage with a callable loan. That rules out buying stocks on margin by borrowing from a broker. You will be forced to sell your stock when it is down, the worst time sell. That is definitely the road to ruin.
Or...you could leverage less than 2x.
Or leverage a portfolio that is not just stocks.

longinvest
Posts: 3288
Joined: Sat Aug 11, 2012 8:44 am

### Re: On Leverage

dknightd wrote:
Fri Feb 15, 2019 7:54 pm
longinvest wrote:
Fri Feb 15, 2019 6:44 pm
dknightd wrote:
Fri Feb 15, 2019 6:20 pm
I'm leveraging my house, but not my retirement investments. If you put them together, then in effect I am leveraging my investments.
I disagree.

We used to own a condo. We had paid off the mortgage within a few years of buying it.

A few years ago we finally realized that owning wasn't our thing. Everybody had always told us that owning was the right financial decision, but we had reached the point where we didn't mind if renting was more expensive or not. We wanted out of real estate ownership.

We sold. Our portfolio immediately grew as if we had remained owners and had taken a new mortgage on the condo.

So, here's my question: is our bigger portfolio leveraged?

If not, why would have it been leveraged if we had remained owners and taken a mortgage equal to the value of the condo minus real estate agent commission? In both cases, the portfolio's starting value would be identical, and the return on it identical too.

The reality is that the portfolio isn't leveraged in either case.

Whether selling and renting or remortgaging wins will be fully determined by the outcome of the real estate investment relative to the cost of renting. The investment portfolio has nothing to do with the better or worse financial outcome.

As I said, the mortgage leverages the real estate investment.
Agreed. But you sold off one investment (condo) and used the money someplace else. I still owe money on my house, which means I'm leveraged. Am I missing something?
If you had taken out a loan on your previously fully paid off condo, I think you would be leveraged. i.e. You are borrowing money against one asset to buy another asset.

I must be missing something?
You're not leveraged; your house is.

The risk introduced by the mortgage is against the house. The portfolio has nothing to do with it. You could have used the money to buy a car, instead; you would still owe the money and the bank could foreclose on the house.
Last edited by longinvest on Fri Feb 15, 2019 8:38 pm, edited 2 times in total.

dknightd
Posts: 1365
Joined: Wed Mar 07, 2018 11:57 am

### Re: On Leverage

longinvest wrote:
Fri Feb 15, 2019 8:12 pm

IYou're not leveraged; your house is.

The risk introduced by the mortgage is against the house. The portfolio has nothing to do with it. You could have used the money to buy a car, instead; you would still owe the money and the bank could foreclose on the house.
True. But I could easily pay off my home loan if I wanted to. Using money from my retirement savings.

I guess diversification is a good thing

MotoTrojan
Posts: 3535
Joined: Wed Feb 01, 2017 8:39 pm

### Re: On Leverage

grayfox wrote:
Fri Feb 15, 2019 10:11 am
aristotelian wrote:
Fri Feb 15, 2019 9:49 am
305pelusa wrote:
Fri Feb 15, 2019 9:45 am

I'm convinced it's a loser's game and succeeds only if you can speculate properly. I'm certainly open to someone changing my mind though.
Did you never carry a mortgage and invest at the same time?
That is another good thought.

Seeing that 2x leverage will go bust when the market drops by -50%, and knowing that it happened in the past, that would mean that you definitely don't want to leverage with a callable loan. That rules out buying stocks on margin by borrowing from a broker. You will be forced to sell your stock when it is down, the worst time sell. That is definitely the road to ruin.

But, as you suggest, if you borrow against your house, I'm pretty sure that is non-callable. That might be something to consider.

My takeaway here is do not get leverage with a callable loan. You never want to be forced to sell.
A daily rebalancing 2x leveraged fund will not go to 0% if the market drops 50%, unless it occurs in one day.

305pelusa
Posts: 181
Joined: Fri Nov 16, 2018 10:20 pm

### Re: On Leverage

AlohaJoe wrote:
Fri Feb 15, 2019 7:45 pm
305pelusa wrote:
Fri Feb 15, 2019 6:31 pm
Imagine you're given a loan. If you invest that money in purely one asset (stocks) I think you run into serious volatility drag. That's purely leverage.
Imagine I am 100% stocks. Then I take out a \$200,000 margin loan from my broker. That leaves me at 120% stocks and -20% cash. Then I use that cash to pay for an extravagant vacation.

Am I really not leveraged? Even though my broker and the SEC consider me leveraged?

Or are you saying that the source of collateral for a loan is what determines whether you have a leveraged portfolio?
There's some semantics here. When I think of "leverage" or a "leveraged position", I'm thinking of borrowing money to invest. Lots of times for short term purposes but, like in this discussion, it can be longer term. From my very small understanding of leveraged investing, that new asset you invest in becomes the collateral.

If you take out a loan and use it to buy a vacation, I do not think of that as a "leveraged position" in the traditional sense. I just think of that as consumer debt. Perhaps from the broker's perspective, he does consider it a leverage.

So from my personal definition of leverage, yes, I think the collateral for the loan determines whether I would call that "leveraged" or just simply a debt. But again, perhaps from the SEC it's all the same from their end. So maybe it's just semantics here ?

alex_686
Posts: 4421
Joined: Mon Feb 09, 2015 2:39 pm

### Re: On Leverage

305pelusa wrote:
Fri Feb 15, 2019 9:51 pm
If you take out a loan and use it to buy a vacation, I do not think of that as a "leveraged position" in the traditional sense. I just think of that as consumer debt. Perhaps from the broker's perspective, he does consider it a leverage.

So from my personal definition of leverage, yes, I think the collateral for the loan determines whether I would call that "leveraged" or just simply a debt. But again, perhaps from the SEC it's all the same from their end. So maybe it's just semantics here ?
It is not a brokerage or SEC thing, it is a economics and rational man thing. Money is fungible, you could chose to liquidate part of your assets and pay down your consumer debt.

Note - it does not matter if you do ir don’t- your net worth is the same. Hence with the consumer debt you are leveraged.

Note - if you don’t think you are leveraged you have fallen into the “mental accounting” fallacy. Ir maybe the framing fallacy.

305pelusa
Posts: 181
Joined: Fri Nov 16, 2018 10:20 pm

### Re: On Leverage

alex_686 wrote:
Sat Feb 16, 2019 7:45 am
305pelusa wrote:
Fri Feb 15, 2019 9:51 pm
If you take out a loan and use it to buy a vacation, I do not think of that as a "leveraged position" in the traditional sense. I just think of that as consumer debt. Perhaps from the broker's perspective, he does consider it a leverage.

So from my personal definition of leverage, yes, I think the collateral for the loan determines whether I would call that "leveraged" or just simply a debt. But again, perhaps from the SEC it's all the same from their end. So maybe it's just semantics here ?
It is not a brokerage or SEC thing, it is a economics and rational man thing. Money is fungible, you could chose to liquidate part of your assets and pay down your consumer debt.

Note - it does not matter if you do ir don’t- your net worth is the same. Hence with the consumer debt you are leveraged.

Note - if you don’t think you are leveraged you have fallen into the “mental accounting” fallacy. Ir maybe the framing fallacy.
No mental accounting here boss. The dictionary definition of "leverage" is as follows:

"use borrowed capital for (an investment), expecting the profits made to be greater than the interest payable."

You might THINK consumer debt is leverage; but I don't think it is by definition.

Topic Author
grayfox
Posts: 5046
Joined: Sat Sep 15, 2007 4:30 am

### Re: On Leverage

A lot of good comments. I don't know if having a mortgage and also buying stocks is technically leveraging the stocks or leveraging the house or something else. It seems to me that you are really borrowing against your future income, using the house as collateral. If you lose your source of income, the bank can take the house and sell it to get their money back.

But anyway, it seems that there are two main issues to consider with leverage:

1. You are borrowing money, so a big issue is the terms of the loan. Who are you borrowing from? How much can you borrow? Collateral required? Interest rate? What period, short term or long term? Recallable? Upfront fees? etc.

2. The portfolio to invest in, which is going to determine the probability distribution of outcomes that you are leveraging up.

Regarding the borrowing, just to have some numbers to work with, for now I am just going to assume that you have equity in a house that you can borrow against and some other source of income to pay the mortgage. It may not be the ideal way to borrow money for leveraging stocks, because you can only borrow to the extent that you have equity in your house, plus have income to make the mortgage payments. Also there are a lot of fees and upfront costs with home mortgages.

Looking on https://www.bankrate.com, they show different option: mortgage loans for purchase, for refinance and home equity. Some examples:

February 2019
purchase mortgage 30-year fixed 4.625% upfront fees = \$1,932
purchase mortgage 15-year fixed 3.875% upfront fees = \$1,932
refinance mortgage 30-year fixed 4.250% upfront fees = \$675
home equity 30-year fixed 4.490%

Somewhere in the neighborhood of 4 - 4-1/2 percent for a 15 or 30 year fixed mortgage.

Again, there may be better options for borrowing than a home mortgage, but I'll just use this for now to have some numbers to work with.

longinvest
Posts: 3288
Joined: Sat Aug 11, 2012 8:44 am

### Re: On Leverage

The problem with debt is that it can easily play games with our brains.

We use a mortgage to put several hundred thousands of dollars into a single undiversified unmovable investment with huge bid-ask spreads and high transaction fees. An investment so risky that we have to insure it. An investment that carries ongoing costs that increase over time. An investment that brings a constant stream of hassles. Yet, the mortgage hides all this and lets us believe that our cost was only the down payment, that the carrying costs and mortgage payment are our rent, and that we've smartly beaten the system by gaining low-rate uncallable leverage for our investment portfolio!

Buying a house, with (or without) a mortgage, can be a good decision. But, believing that the mortgage isn't leverage against the considerable amount of money that was given to the seller, when we bought the the house, is a form of mental accounting.

A rational analysis, like I presented earlier in this thread, makes clear that the mortgage is leveraging the house, not the investment portfolio.

Topic Author
grayfox
Posts: 5046
Joined: Sat Sep 15, 2007 4:30 am

### Re: On Leverage

As far as the second issue, what to invest in, my thinking is this. Since leverage multiples the variance, i.e. makes the probability distribution wider, you will want to start with a distribution that has low variance. The ideal distribution would have an expected return of maybe 10% with the worst case being 9% and the best case being 11%. I would borrow as much as possible to invest in that!

Unfortunately, no such asset exists. You can get a low variance, e.g. 12-month T-bill, but the return right now is only 2.56%. It seems to me that the expected return has to be greater than the borrowing cost, which I'm assuming is 4% p.a., in order for leverage to make sense. And Treasuries across the board all the way out to 30 years are all less than about 3%. So forget about leveraging Treasuries. That might make sense if I could borrow at 0.1% like the banks, but borrowing with a mortgage at 4% it doesn't work.

What I would be looking for is an asset that has low variance. Like with standard deviation in the single digits. That way when you multiple x2 or x3, the result is not too high. In fact, all that really matters is how far to the left it goes. So maybe I would look at the worst year and max drawdown. Try to keep the Max Drawdown to a dull roar. Maybe about -10 percent. Multiplying x2 with leverage would make Max DD about -20 percent.

Plus a constraint that the expected return has to be greater than the borrowing cost, which I'm assuming is about 4%.

Here is the criteria: Find asset with low MAX DD with expected return greater than about 4%.
Last edited by grayfox on Sat Feb 16, 2019 10:09 am, edited 1 time in total.

Stormbringer
Posts: 750
Joined: Sun Jun 14, 2015 7:07 am

### Re: On Leverage

grayfox wrote:
Fri Feb 15, 2019 8:50 am
I've never bought stocks on margin or used leverage in investing
You probably have used leverage and didn't realize it. Most publicly traded corporations borrow significant amounts of money to fund investments and stock repurchases. So when you buy them with leverage, you are leveraging an already leveraged asset.

The reason companies like AAPL who are awash in profits use leverage is to reduce their weighted average cost of capital.
"Compound interest is the most powerful force in the universe." - Albert Einstein

pezblanco
Posts: 595
Joined: Thu Sep 12, 2013 8:02 pm

### Re: On Leverage

What you want to use is the Kelly Criterion to give you an idea of whether leverage is going to be feasible. The dispersion of the returns and the expected values are of course key and the KC takes those into account in a systematic way.

HEDGEFUNDIE
Posts: 2077
Joined: Sun Oct 22, 2017 2:06 pm

### Re: On Leverage

grayfox wrote:
Sat Feb 16, 2019 9:59 am
As far as the second issue, what to invest in, my thinking is this. Since leverage multiples the variance, i.e. makes the probability distribution wider, you will want to start with a distribution that has low variance. The ideal distribution would have an expected return of maybe 10% with the worst case being 9% and the best case being 11%. I would borrow as much as possible to invest in that!

Unfortunately, no such asset exists. You can get a low variance, e.g. 12-month T-bill, but the return right now is only 2.56%. It seems to me that the expected return has to be greater than the borrowing cost, which I'm assuming is 4% p.a., in order for leverage to make sense. And Treasuries across the board all the way out to 30 years are all less than about 3%. So forget about leveraging Treasuries. That might make sense if I could borrow at 0.1% like the banks, but borrowing with a mortgage at 4% it doesn't work.

What I would be looking for is an asset that has low variance. Like with standard deviation in the single digits. That way when you multiple x2 or x3, the result is not too high. In fact, all that really matters is how far to the left it goes. So maybe I would look at the worst year and max drawdown. Try to keep the Max Drawdown to a dull roar. Maybe about -10 percent. Multiplying x2 with leverage would make Max DD about -20 percent.

Plus a constraint that the expected return has to be greater than the borrowing cost, which I'm assuming is about 4%.

Here is the criteria: Find asset with low MAX DD with expected return greater than about 4%.
What’s holding you back is you are looking for a single asset that meets your criteria (which as you say, doesn’t exist).

The solution is to build a diversified portfolio of assets that, in the aggregate, exhibit high return and low volatility. This is a doable task. Diversification is the only free lunch.

Topic Author
grayfox
Posts: 5046
Joined: Sat Sep 15, 2007 4:30 am

### Re: On Leverage

OK, So I headed over to portfoliovisualizer.com which lets you back test portfolios. I went to Backtest Asset Allocation which backtests generic asset classes. Then it gives you a graph and all the statistics like CAGR Steve Max DD, etc. First I looked at various stock asset classes.

Code: Select all

``````Asset Class             Since   CAGR    STD DEV BEST    WORST   MAX DD  SHARPE
US Stock Market         1972    10.22   15.40   37.82   -37.04  -50.89  0.41
US Large Cap            1972    10.15   15.09   37.45   -37.02  -50.97  0.42
US Large Cap Value      1972    11.19   14.73   40.67   -35.97  -54.85  0.49
US Large Cap Growth     1972    9.88    16.66   44.61   -38.32  -53.60  0.38
Global ex-US Stock      1986    6.84    17.79   63.38   -44.10  58.50   0.29
Intl Developed ex US    1986    6.89    17.44   63.38   -41.27  -57.06  0.29
Emerging Market         1995    6.01    22.84   75.98   -52.81  -62.70  0.27
REIT                    1994    9.32    19.26   35.66   -37.05  -68.28  0.44
Gold                    1972    7.37    20.20   126.55  -32.60  -61.78  0.22``````
They all had double-digit standard deviations of 15 or 20 and Max DD of -50 or -60 percent. Those assets are too hot to leverage. You will be wiped out in the next market crash.

Next I looked at generic bonds asset classes.

Code: Select all

``````Asset Class                     Since   CAGR    STD DEV BEST    WORST   MAX DD  SHARPE
Short Term Treasury             1977    5.91    3.13    22.12   -0.48   -4.26   0.47
Intermediate Term Treasury      1972    6.96    5.84    31.13   -4.33   -10.70  0.41
10-year Treasury                1972    7.07    8.10    39.57   -10.17  -15.76  0.32
Long Term Treasury              1978    8.29    10.96   47.10   -13.03  -23.12  0.38
Total US Bond                   1987    5.79    3.81    18.18   -2.66   -5.86   0.71
TIPS                            2001    4.77    5.90    16.61   -8.92   -12.50  0.59
Global Bonds (Unhedged)         1994    5.58    6.77    22.91   -6.36   -17.49  0.49
Global Bonds (USD Hedged)       1999    5.51    3.57    15.30   -2.35   -10.03  1.02
Short Term Investment Grade     1983    5.87    2.47    14.90   -4.74   -7.61   0.93
Corporate Bonds                 2003    5.03    7.21    10.58   -3.79   -15.11  -0.55
Long Term Corporate Bonds       1974    8.20    8.04    28.68   6.23    -16.82  0.46
High Yield Corporate Bonds      1979    8.26    7.37    39.09   -21.29  -28.90  0.77``````
Except for the LT Treasuries, all the bonds had single-digit SD. ST Treasury, Total US Bond and ST Investment grade all had less than 10% Max DD. Those look promising. So I looked at some equivalent Vanguard funds:

Code: Select all

``````Fund            Symbol  Since           CAGR    STD DEV BEST    WORST   MAX DD  SHARPE  S.E.C.
VG ST Treasury  VFISX   Jan-1992        3.79    1.95    12.11   -0.48   -2.23   0.72    2.38
VG Total Bond t VBMFX   Jan-1987        5.79    3.81    18.18   -2.66   -5.86   0.71    3.16
VG ST Inv Grade VFSTX   Jan-1985        5.54    2.35    14.90   -4.74   -7.61   0.97    3.09
VG LT Treasury  VUSTX   Jan-1987        7.26    9.63    30.09   -13.03  -16.68  0.46    2.80
VG 500 Index    VFINX   Jan-1985        10.90   14.85   37.45   -37.02  -50.97  0.56
VG GlobalMinVol VMNVX   Jan-2014        9.38    7.42    16.07   -1.73   -8.23   0.90``````
Very low SD and Max DD. But then I looked up the S.E.C. Yield on Vanguard which is the last column.
If S.E.C is the expected return, they are all below 4%. Too low.

All the stocks are too hot and all the bonds are too cold.
Last edited by grayfox on Thu Feb 21, 2019 11:47 am, edited 1 time in total.

Topic Author
grayfox
Posts: 5046
Joined: Sat Sep 15, 2007 4:30 am

### Re: On Leverage

HEDGEFUNDIE wrote:
Sat Feb 16, 2019 10:53 am
The solution is to build a diversified portfolio of assets that, in the aggregate, exhibit high return and low volatility. This is a doable task. Diversification is the only free lunch.
OK, I will try your idea. I decided to try some of Vanguard's balanced funds.

Code: Select all

``````Fund            Symbol  Since           CAGR    STD DEV BEST    WORST   MAX DD  SHARPE
60/40 VFINX/VUSTX       Jan-1987        9.54    9.40    34.50   -13.21  -26.96  0.69
VG Bal Index    VBINX   Jan-1993        7.90    8.85    28.64   -22.21  -32.57  0.64
VG Wellington   VWELX   Jan-1985        10.33   9.88    32.92   -22.30  -32.53  0.72

40/60 VFINX/VUSTX       Jan-1987        8.96    7.99    33.03   -3.75   -14.52  0.74
VG Wellesley    VWINX   Jan-1985        9.31    6.51    28.91   -9.84   -18.82  0.91
VG TargRetInc   VTINX   Jan-2004        4.95    5.05    14.28   -10.93  -17.00  0.74
Harry Browne Perm Port   Dec-2004	6.57    6.54    13.94   -2.63   -13.36  0.82    1/4 VFINX/VUSTX/VFISX/GLD``````
All single-digit SD. Max DD more than -10%, but Wellesley and Target Retirement Income are less than -20% Max DD. If you leverage that up 2x or 3x it would still only be Max DD -40 or -60 percent. You could probably leverage them up even 5x without going bust.

What is the expected return of Wellesley and Target Retirement Income? Wellesley CAGR since 1985 shows 9.31% p.a. So I'm guessing more than 4% going forward.

This is getting to be like the Goldilocks story. Stocks are too hot. Bonds are too cold. Balanced Fund is just right.
Last edited by grayfox on Sun Feb 24, 2019 7:24 am, edited 3 times in total.

pezblanco
Posts: 595
Joined: Thu Sep 12, 2013 8:02 pm

### Re: On Leverage

The benefits of leverage are wildly overstated ..... People have this idea that well, stocks give 6 percent real and I can borrow at 2 percent over the inflation rate so that means I clear 4 percent real on the leveraged money. So, that's 4% per unit of leverage ... off to infinity right? The more leverage the better.

But investment returns over a long period are a non-linear function (mulitiplicative, with logarithms) of their unit time period returns. They don't scale linearly. There are theoretical limits to how much leverage due to the volatility of those returns. For example, leveraging up the S&P 500 gives you at MOST about .5% or return (based on real return data from the last 50 years).

I did some recent calculations in another thread:

viewtopic.php?f=10&t=273154

With leverage to get even those modest gains, you have to accept a greatly increased negative tail risk .... Leverage is not by any means a free lunch.

2015
Posts: 2855
Joined: Mon Feb 10, 2014 2:32 pm

### Re: On Leverage

grayfox wrote:
Sat Feb 16, 2019 11:31 am
OK, So I headed over to portfoliovisualizer.com which lets you back test portfolios. I went to Backtest Asset Allocation which backtests generic asset classes. Then it gives you a graph and all the statistics like CAGR Steve Max DD, etc. First I looked at various stock asset classes.

Code: Select all

``````Asset Class             Since   CAGR    STD DEV BEST    WORST   MAX DD  SHARPE
US Stock Market         1972    10.22   15.40   37.82   -37.04  -50.89  0.41
US Large Cap            1972    10.15   15.09   37.45   -37.02  -50.97  0.42
US Large Cap Value      1972    11.19   14.73   40.67   -35.97  -54.85  0.49
US Large Cap Growth     1972    9.88    16.66   44.61   -38.32  -53.60  0.38
Global ex-US Stock      1986    6.84    17.79   63.38   -44.10  58.50   0.29
Intl Developed ex US    1986    6.89    17.44   63.38   -41.27  -57.06  0.29
Emerging Market         1995    6.01    22.84   75.98   -52.81  -62.70  0.27
REIT                    1994    9.32    19.26   35.66   -37.05  -68.28  0.44
Gold                    1972    7.37    20.20   126.55  -32.60  -61.78  0.22``````
They all had double-digit standard deviations of 15 or 20 and Max DD of -50 or -60 percent. Those assets are too hot to leverage. You will be wiped out in the next market crash.

Next I looked at generic bonds asset classes.

Code: Select all

``````Asset Class                     Since   CAGR    STD DEV BEST    WORST   MAX DD  SHARPE
Short Term Treasury             1977    5.91    3.13    22.12   -0.48   -4.26   0.47
Intermediate Term Treasury      1972    6.96    5.84    31.13   -4.33   -10.70  0.41
10-year Treasury                1972    7.07    8.10    39.57   -10.17  -15.76  0.32
Long Term Treasury              1978    8.29    10.96   47.10   -13.03  -23.12  0.38
Total US Bond                   1987    5.79    3.81    18.18   -2.66   -5.86   0.71
TIPS                            2001    4.77    5.90    16.61   -8.92   -12.50  0.59
Global Bonds (Unhedged)         1994    5.58    6.77    22.91   -6.36   -17.49  0.49
Global Bonds (USD Hedged)       1999    5.51    3.57    15.30   -2.35   -10.03  1.02
Short Term Investment Grade     1983    5.87    2.47    14.90   -4.74   -7.61   0.93
Corporate Bonds                 2003    5.03    7.21    10.58   -3.79   -15.11  -0.55
Long Term Corporate Bonds       1974    8.20    8.04    28.68   6.23    -16.82  0.46
High Yield Corporate Bonds      1979    8.26    7.37    39.09   -21.29  -28.90  0.77``````
Except for the LT Treasuries, all the bonds had single-digit SD. ST Treasury, Total US Bond and ST Investment grade all had less than 10% Max DD. Those look promising. So I looked at some equivalent Vanguard funds:

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``````Asset Class             Since   CAGR    STD DEV BEST    WORST   MAX DD  SHARPE  SEC
VG ST Treasury VFISX    1992    3.79    1.95    12.11   -0.48   -2.23   0.72    2.38
VG Total Bond VBMFX     1987    5.79    3.81    18.18   -2.66   -5.86   0.71    3.16
VG ST Invest Gr VFSTX   1985    5.54    2.35    14.90   -4.74   -7.61   0.97    3.09 ``````
Very low SD and Max DD. But then I looked up the S.E.C. Yield on Vanguard which is the last column.
If S.E.C is the expected return, they are all below 4%. Too low.

All the stocks are too hot and all the bonds are too cold.
I always get a kick out these threads. I've posted elsewhere I think there will always be newcomers attracted to BH because of the stock market emphasis (greed, ego). Your response post to me up thread attempting to conflate the "free lunch" of diversification with leverage is almost comical (almost, if it weren't so tragic).

In my mind, Portfoliovisualizer is the handle on the slot machine in the casino because it keeps the addict pulling on the lever in an almost pathological search for certainty in a certainly uncertain world. It sometimes often helps to go outside the fields of investing, personal finance, and microeconomics to see how easily we humans can fool our overconfident selves. Ironically, this quote from the linked article on the reasons for judgment failure in a complex system can just as easily apply to anything related to investing:
“It is just a dynamic resource theme, a dynamic time in the industry where so much is changing so fast. That it makes it hard for anyone to take a snapshot and say this is what informs me about the future," says Wood Mackenzie analyst R.T. Dukes.
https://www.axios.com/experts-consisten ... e6ef2.html

305pelusa
Posts: 181
Joined: Fri Nov 16, 2018 10:20 pm

### Re: On Leverage

grayfox wrote:
Sat Feb 16, 2019 11:31 am
All the stocks are too hot and all the bonds are too cold.
It's a shame lender rates are higher than bond rates huh? Otherwise we could just borrow money (leverage) and then lend that same money (buy bonds) and make a profit. That would have been some real easy money huh?

Topic Author
grayfox
Posts: 5046
Joined: Sat Sep 15, 2007 4:30 am

### Re: On Leverage

OK, here is what I have so far:

Eight Simple Rules for Leveraging My Retirement Portfolio

1. Borrow at the best terms possible. Among other things, this means low interest rate, low fees and non-callable. The lower the rate, the more profit. (I don't know the best place to borrow money. The only thing I can think of is take out a mortgage on your home.)

2. Don't leverage highly volatile investments like stocks. It multiplies an already high variance and will blow up on you.

3. Unless you can get very cheap money, you can't leverage safe assets like Treasuries because their return is too low. The return has to be more than the rate you can borrow at.

4. Leverage something like Wellesley Income VWINX. This is about 38% stocks / 60% bonds / 2% cash. As Goldilocks would say, It is neither too hot nor too cold, but just right.

5. The key factor to look at is the difference between the rate you can borrow at and the rate of return on the investment, a.k.a. the spread. You want to borrow at low rate and invest at high rate, and you want the spread to be wide. If you don't have a wide spread forget it. Don't try to multiple up a narrow spread with a greater amount of leverage.

8. How much leverage? This is above my pay grade. Poster pezblanco did the math and says to use the Kelly Criterion which takes the dispersion of the returns and the expected values into account in a systematic way. According to the other thread, the optimal leverage is about 3.2:1 for 40/60 S&P500 / LT Treasuries.
Last edited by grayfox on Thu Feb 21, 2019 7:22 am, edited 1 time in total.

Topic Author
grayfox
Posts: 5046
Joined: Sat Sep 15, 2007 4:30 am

### Re: On Leverage

I'm wondering how it would have worked out if you had leveraged Wellesley Income VWINX. Well, I learned a trick from another thread. It turns out that you can use portfoliovisualer to simulate leveraged portfolios. Let's say you want 2x leverage. All you have to do is enter 200% for VWINX and -100% for CASHX. I believe CASHX is some kind of average money market return for CASH. So -100% CASHX is like borrowing at the average money market rate.

I compared portfolios with VWINX/CASHX for no leverage, 2:1 leverage, and 3:1 leverage from Jan-1985 to Jan-2019. I also included 100% S&P 500 VFINX as a benchmark.

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``````VWINX/CASHX     Initial Final Balance   CAGR    Stdev   Best    Worst   Max. Drawdown   Sharpe
100/0           \$10,000 \$207,601        9.31%   6.51%   28.91%  -9.84%  -18.82%         0.91
200/-100        \$10,000 \$1,053,801      14.64%  12.76%  51.73%  -21.16% -37.10%         0.89
300/-200        \$10,000 \$4,262,610      19.44%  19.16%  74.54%  -32.48% -52.89%         0.86

100% VFINX      \$10,000 \$340,134        10.90%  14.85%  37.45%  -37.02% -50.97%         0.56``````
With 2:1 and 3:1 leverage, CAGR, Stdev, Best Year, Worst Year, Max DD all increased.
With 2:1 leverage, Max DD went from about -19% to -37%. That's similar to a typical 75/25 stock/bond portfolio.
With 3:1 leverage, VWINX has slightly more Max DD than 100% S&P 500 Index Fund.

Leveraging Wellesley Income 2:1 or even 3:1 does not seem all that risky. At least compared to 100% S&P 500, which plenty of people have. You probably want a margin-of-safety of at least a factor of 2x in case there are worse drawdowns than the period 1985-2019.

So how much could you have leveraged VWINX before it blows up ? I decided to stress test it.

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``````VWINX/CASHX     Initial Final Balance   CAGR    Stdev   Best    Worst   Max. Drawdown   Sharpe
100/0           \$10,000 \$207,601        9.31%   6.51%   28.91%  -9.84%  -18.82%         0.91
200/-100        \$10,000 \$1,053,801      14.64%  12.76%  51.73%  -21.16% -37.10%         0.89
300/-200        \$10,000 \$4,262,610      19.44%  19.16%  74.54%  -32.48% -52.89%         0.86
400/-300        \$10,000 \$13,975,494     23.68%  25.95%  97.36%  -43.80% -66.27%         0.83
500/-400        \$10,000 \$37,217,752     27.28%  33.90%  120.17% -55.12% -77.34%         0.80
600/-500        \$10,000 \$79,099,356     30.13%  48.54%  142.99% -66.44% -89.54%         0.71
700/-600        \$10,000 \$0.00           N/A     50.07%  165.81% -100.00%        N/A     0.53   <- terminated Oct-2008``````
It worked all the way up to 6:1 leverage, which had -89.54% MAX DD.
With 7:1 leverage, it blowed up good!
And when did it blowed up? Yep, October 2008. Who would have guessed?

The only fly in the ointment is that this simulates borrowing at money market rates. I don't think the average investor can borrow at such low rates. That would be like borrowing at 2-2.5% today. More likely today you could only borrow at 4-5%. So you need cheap money to pull this off.

pezblanco
Posts: 595
Joined: Thu Sep 12, 2013 8:02 pm

### Re: On Leverage

Super interesting grayfox!

A few comments on why I would worry about drawing conclusions from this ....

1) During that 34 year time period 1985 to present, the S&P 500 returned 8.33% real. Over 50 years that drops to 5.9% real. This is
a time period in which stocks have done exceptionally well.
2) As you noted, the interest rate is not realistic. The cost to borrow rate is critical in trying to evaluate a leverage strategy.
It affects the results QUALITATIVELY. Just a question ... I don't use PV very often. Could you put in -100% of some intermediate term
bond fund? That might give you something closer to a more realistic borrow rate.
3) The fund you are leveraging is a 40/60 fund. Taking the last 34 years as independent samples of returns that you will get in the future, the Kelly criterion gives you the following leverage vs. return graph. I don't trust this result at all .... just not enough representative data

It gives a an optimal leverage of around 9!! So, in the ballpark of what you are seeing. Again the borrow rate here is assumed to be 1.5% + T-bill rate. (Note: the result given here is for leveraging the S&P 500 ... not the Vanguard fund .... so things are expected to be different)

comeinvest
Posts: 182
Joined: Mon Mar 12, 2012 6:57 pm

### Re: On Leverage

grayfox wrote:
Sun Feb 17, 2019 7:43 am
OK, here is what I have so far:

4. Leverage something like Wellesley Income VWINX. This is about 38% stocks / 60% bonds / 2% cash. As Goldilocks would say, It is neither too hot nor too cold, but just right.
During the past few decades, interest rates tanked and bonds went up, so this worked maybe. Going forward, extrapolation of this scenario is mathematically almost impossible. Therefore this backtest is totally meaningless.
More specifically, going forward, you would essentially be leveraging lower yielding bonds with a higher yielding (as 305pelusa pointed out above) mortgage. Congratulations on the non-callable loan ... which would almost guarantee negative arbitrage in combination with the "bond" portion of your hybrid fund.

In contrast to many other posters above, I am questioning the utility of non-callable loans for purpose of leverage, due to too high interest rates. Portfolio margin loans at lower interest rates can be used for moderate long term leverage with a much higher profit margin, while still avoiding volatility decay by abandoning constant leverage but rather using a fixed borrowed amount.

Topic Author
grayfox
Posts: 5046
Joined: Sat Sep 15, 2007 4:30 am

### Re: On Leverage

pezblanco wrote:
Mon Feb 18, 2019 10:32 am

2) As you noted, the interest rate is not realistic. The cost to borrow rate is critical in trying to evaluate a leverage strategy.
It affects the results QUALITATIVELY. Just a question ... I don't use PV very often. Could you put in -100% of some intermediate term
bond fund? That might give you something closer to a more realistic borrow rate.
OK, I decided to try Vanguard GNMA Fund VFIIX instead of CASHX. VFIIX is 90% government mortgage-backed bonds. The portfolio is long VWINX and short VFIIX. Maybe this simulates paying higher interest rate. Here is VWINX/VFIIX

Code: Select all

``````VWINX/VFIIX     Initial Final Balance   CAGR    Stdev   Best    Worst   Max. Drawdown   Sharpe
100/0           \$10,000 \$207,601        9.31%   6.51%   28.91%  -9.84%  -18.82%         0.91
200/-200        \$10,000 \$427,291        11.65%  11.31%  40.37%  -26.45% -42.47%         0.75
300/-300        \$10,000 \$767,812        13.58%  16.65%  51.84%  -43.05% -61.94%         0.66
400/-300        \$10,000 \$1,169,341      14.99%  22.68%  63.30%  -59.65% -77.58%         0.59
500/-400        \$10,000 \$1,377,169      15.55%  31.55%  74.76%  -76.25% -89.30%         0.52
575/-475        \$10,000 \$1,053,821      14.64%  1,292.92%       83.36%  -88.71% -99.88%         0.18
576/-576        \$10,000 \$0.00           N/A     38.31%  83.47%  -100.00%        N/A     0.20``````
Compare against the previous results that used VWINX/CASHX

Code: Select all

``````VWINX/CASHX     Initial Final Balance   CAGR    Stdev   Best    Worst   Max. Drawdown   Sharpe
100/0           \$10,000 \$207,601        9.31%   6.51%   28.91%  -9.84%  -18.82%         0.91
200/-100        \$10,000 \$1,053,801      14.64%  12.76%  51.73%  -21.16% -37.10%         0.89
300/-200        \$10,000 \$4,262,610      19.44%  19.16%  74.54%  -32.48% -52.89%         0.86
400/-300        \$10,000 \$13,975,494     23.68%  25.95%  97.36%  -43.80% -66.27%         0.83
500/-400        \$10,000 \$37,217,752     27.28%  33.90%  120.17% -55.12% -77.34%         0.80
600/-500        \$10,000 \$79,099,356     30.13%  48.54%  142.99% -66.44% -89.54%         0.71
700/-600        \$10,000 \$0.00           N/A     50.07%  165.81% -100.00%        N/A     0.53   <- terminated Oct-2008``````
Using VFIIX instead of CASHX, CAGR and the final balances are much lower. Less than half for 2:1. So not as much reward.
At the same time, MAX DD increased , so I would say the risk went up.

And the amount of leverage before it blew up was also less. Up to 5.75:1 where the MAX DD was -99.88% which was in Oct-2008.
At 5.76:1 leverage, it blew up in Nov-2008.

2:1 Leverage with VWINX borrowing at mortgage rates seems about as risky as 100% S&P500.

My takeaway from using VFIIX versus CASHX is the higher the interest rate you pay to borrow, the lower your return, and the greater your risk. And less leverage before it blows up.

Topic Author
grayfox
Posts: 5046
Joined: Sat Sep 15, 2007 4:30 am

### Re: On Leverage

comeinvest wrote:
Tue Feb 19, 2019 7:11 am

In contrast to many other posters above, I am questioning the utility of non-callable loans for purpose of leverage, due to too high interest rates. Portfolio margin loans at lower interest rates can be used for moderate long term leverage with a much higher profit margin, while still avoiding volatility decay by abandoning constant leverage but rather using a fixed borrowed amount.
Right. Risk and return seems to be very sensitive to the interest rate you can borrow at. I am beginning to think that leverage only makes sense when the interest rate is quite low compared to what you are leveraging. Mortgage rates may not be low enough for leverage to be worthwhile.

SovereignInvestor
Posts: 17
Joined: Mon Aug 20, 2018 4:41 pm

### Re: On Leverage

A mortgage on house is leverage because it is debt. It allows someone with more upfront cash available for imvestment or other things than otherwise if they paid it off.

However, technically renting is leverage too because it is a debt, most companies must disclose leases as liabilities on their balance sheet.

If one rents as long as they want any place to love they will have a liability in the form of rent.

However going from renting to then buying a house with mortgage is often not a change in net liability or leverage, since one removes the renting/lease liability and replaces it with mortgage, taxes, insurance etc.

Generally the house owning liability is a bit larger so leverage does increase but it is generally removing one liability (lease liability) and adding a bigger one.

If one has a fully paid for house, their dramatically reduce their liability since it's only upkeep as a future liability.

With that said a mortgage is likely made the safest leverage since it can be fixed rate and 30 years and have a lower rate since it's secured by real property and interest is often deductible.

Jayhawker
Posts: 6
Joined: Fri Jan 18, 2019 4:45 pm

### Re: On Leverage

SovereignInvestor wrote:
Tue Feb 19, 2019 8:41 am
A mortgage on house is leverage because it is debt. It allows someone with more upfront cash available for imvestment or other things than otherwise if they paid it off.

However, technically renting is leverage too because it is a debt, most companies must disclose leases as liabilities on their balance sheet.

If one rents as long as they want any place to love they will have a liability in the form of rent.

However going from renting to then buying a house with mortgage is often not a change in net liability or leverage, since one removes the renting/lease liability and replaces it with mortgage, taxes, insurance etc.

Generally the house owning liability is a bit larger so leverage does increase but it is generally removing one liability (lease liability) and adding a bigger one.

If one has a fully paid for house, their dramatically reduce their liability since it's only upkeep as a future liability.

With that said a mortgage is likely made the safest leverage since it can be fixed rate and 30 years and have a lower rate since it's secured by real property and interest is often deductible.
This is interesting. How would one roughly estimate the liability of ongoing rent into the future?