On Leverage

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alex_686
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Re: On Leverage

Post by alex_686 » Tue Feb 19, 2019 7:04 pm

Jayhawker wrote:
Tue Feb 19, 2019 6:59 pm
SovereignInvestor wrote:
Tue Feb 19, 2019 8:41 am
However, technically renting is leverage too because it is a debt, most companies must disclose leases as liabilities on their balance sheet.
This is interesting. How would one roughly estimate the liability of ongoing rent into the future?
One would not. Companies do you report leases on their balance sheet - they only report capital leases. For example, let us say that you entered into a lease agreement where you agree to make monthly lease payments for 30 years, and at the end of that 30 years you could buy your house for $1. That would be a capital lease.

Back in the 90s many companies made their debt on their balance sheet disappear via this slight of hand - converting debt payments for capital leases. Accounting standards got changed so you could no longer do this magic trick.

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grayfox
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Re: On Leverage

Post by grayfox » Wed Feb 20, 2019 7:26 am

Further analysis of leveraging VWINX.

In earlier examples, I did not show the return of CASHX and VFIIX. It might be worth while showing that.

Jan 1985 - Jan 2019

Code: Select all

Portfolio       Initial Final Balance   CAGR    Stdev   Best    Worst   Max. Drawdown   Sharpe Ratio
CASHX           $10,000 $30,454         3.32%   0.74%   8.38%    0.00%   0.00%          N/A
VFIIX           $10,000 $86,848         6.55%   3.59%   20.68%  -2.23%  -6.52%          0.90
VWINX           $10,000 $207,601        9.31%   6.51%   28.91%  -9.84%  -18.82%         0.91
Money market fund CASHX returned 3.32% and GNMA mortgage bond fund VFIIX returned 6.55%. Then if you leverage VWINX 2:1 with either CASHX or VFIIX:

Code: Select all

Portfolio     	Initial Final Balance   CAGR    Stdev   Best    Worst   Max. Drawdown   Sharpe
VWINX/-CASHX	$10,000 $1,053,801      14.64%  12.76%  51.73%  -21.16% -37.10%         0.89
VWINX/-VFIIX	$10,000 $427,291        11.65%  11.31%  40.37%  -26.45% -42.47%         0.75
In the first example, you went short CASHX which had 3.32% CAGR. So that was a loss of -3.32%. But that loss enabled you to buy twice as much VWINX which had a 9.31% CAGR, so overall a larger gain. The gains on VWINX was greater than the loss on CASHX, so overall a huge 14.64% CAGR.

In the second example, you went short VFIIIX which had 6.55% CAGR. So that was a loss of -6.55%, greater magnitude of loss than CASHX. With the same 9.31% CAGR on VWINX, overall your gain was smaller 11.65% CAGR. (With higher borrowing cost (simulated by shorting VFIIX) the return only went from 9.31 to 11.65. Is that worth the added risk?)

In both cases, the amount of leverage was 2:1. But the outcome was different because the borrowing costs were different.

:arrow: You are leveraging up the difference (spread) between what the borrowing cost you and what you gain on the investment. You want that spread to be as wide as possible.

:moneybag If you can borrow at 3% and invest at 9%, you can make money all day. :moneybag

:idea: The spread between borrowing rate and return on the underlying asset is key. Wider spread is better.

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Re: On Leverage

Post by grayfox » Thu Feb 21, 2019 7:40 am

It occurs to me that using leverage is a special case of long/short investing.

If you borrow a share of stock and sell it, you are short that share of stock. And when you are short stock, instead of receiving dividends you have to PAY the dividend amount. By the same token, if you borrow money you are short cash, right? And you have to pay amount of interest it would earn.

When you are short stock, if the stock goes down like you hoped, you can buy it back cheaper, turning the stock's loss into your gain. Meanwhile you are long another stock that you expect to go up. So the spread is the difference between the short's losses and the long's gains. Hopefully very wide. E.g. Short Stock A and Long Stock B. A looses -5%. B gains +10%. Spread = +15%.

But if you are short cash, cash can't go down. So the spread will just be the difference between a smaller gain on the cash and a larger gain on the long investment. E.g. Borrow at 3%. Invest at 9%. Spread = +6%.

:arrow: Leveraging is a milder form of Long/Short Strategy where you are short cash and long the investment.

:idea: I am becoming convinced that having a wide spread is a necessary condition for leverage to be advantageous. Before considering leveraging, I would try to determine what my spread is. So I updated an earlier post to add another leveraging rule:

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.

Famous Case of Leverage Gone Wrong: Long-Term Capital Management. They had a strategy that only made a few basis points, i.e. narrow spread. Then they leverage it 25:1 and made 40% p.a. Stuff happened. Eventually they were leveraged 250:1 and ended up bankrupt.

alex_686
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Re: On Leverage

Post by alex_686 » Thu Feb 21, 2019 3:01 pm

grayfox wrote:
Thu Feb 21, 2019 7:40 am
It occurs to me that using leverage is a special case of long/short investing.
It is not.

When you use leverage your get Beta. i.e., market exposure. That is, your portfolio's return should be: 150% Equity Market - 50% Short Term Bond Rate. Your extra return comes from extra exposure to the equity market. In this case, you have a Beta of 1.5. Running this portfolio requires little skill, you just crank up the risk / return profile of your portfolio.

When you short stocks, you get Alpha. i.e., return attributed to skill. Your portfolio return should be 150% Equity Market - 50 Equity Market, or 100% Equity Market. In this case you have market exposure or a Beta of 1, or exactly the same as if your portfolio was unleveraged. The reason you short the market is because you have specific market expectations of stocks in the market. You can now make twice the choices than a 100% long only market exposure, so you get to double the return attributed to your skill.

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Re: On Leverage

Post by grayfox » Fri Feb 22, 2019 6:29 am

alex_686 wrote:
Thu Feb 21, 2019 3:01 pm
grayfox wrote:
Thu Feb 21, 2019 7:40 am
It occurs to me that using leverage is a special case of long/short investing.
It is not.
OK, I will accept you explanation that leverage and shorting stocks are separate strategies.

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Re: On Leverage

Post by grayfox » Fri Feb 22, 2019 7:02 am

I am sticking with the idea that there must be a wide spread between the borrowing rate and the expected return on the investment to make leverage worthwhile. But how wide is wide enough? Let's look at some numbers:

From portfoliovisualizer data from 1985 to 2019, CASHX returned 3.32% CAGR while VWINX returned 9.31%. Spread = +599 basis points.
2:1 leverage returned 14.64%. Leverage increased return by +533 bsp. So about +600 bsp spread seems to be adequate.

Shorting with VFIIX over the same period. VFIIX returned 6.55% CAGR. With same VWINX return, the spread = +280 bsp
2:1 leverage returned 11.31%. Leverage increased return by +200 basis points. Worthwhile or not? Decided for yourself.
Last edited by grayfox on Fri Feb 22, 2019 7:53 am, edited 1 time in total.

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Re: On Leverage

Post by grayfox » Fri Feb 22, 2019 7:45 am

But the 64 dollar question is: What is the spread TODAY? If I borrow at mortgage rates and invest in Wellesley Income, what is the spread?

I already looked at mortgage rates and found they varied from 3.875% to 4.625%. I'll call the borrowing cost 4%. What about the expected return on Wellesley.

Looking at Vanguard Wellesley Income Fund Investor Shares (VWINX), the asset allocation is 38.05% Stocks / 59.94% Bonds / 2.01% Short-term reserves.

Wellesley holds 1030 bonds with YTM = 3.6% and Average Maturity = 9.5 years. The bonds look to be a mix of Treasuries and Corporate bonds. The benchmark is A or better. I will use the YTM - 3.6% as the expected return of the bond portion.

As far as stocks, Wellesley holds 70 stocks. The benchmark is FTSE High Dividend Yield Index. So I will say that the stock part is somewhat similar to Vanguard High Dividend Yield (VHDYX). P/E is 16.1x and Yahoo Finance shows a dividend yield of 3.12%.

The are all kinds of estimates for the expected return of stocks. Dividend discount model, earnings yield, etc. There is no shortage of forecasts. Pick whichever you like. But a lot of forecasts are around 6%. So I'll go with 6.0%.

Code: Select all

	Alloc	E.R
Stocks	38.05	6.0%
Bonds	59.94	3.6%
ST	 2.01	2.46%
VWINX		4.21%
Expected Return of Wellesley is just over 4%. That is awful close to the borrowing cost, if I used a mortgage. Even if I got the best 15-year rate of 3.875 and VWINX returned 4.21%, 4.21 - 3.875 = 0.34% = 34 basis point spread. Awful slim margin.

Suppose I could borrow at 3-month LIBOR + 1%, which I am hearing. 3-month LIBOR shows as 2.64% this week. A year ago it was 1.90%. The spread would be 4.21 - 3.64 = 57 bsp. Still awful slim.

:arrow: My conclusion is that the spread at this time, +30 to +60 bsp, is too narrow to justify taking on the risk of leverage. Minimum spread I would consider is +250 bsp. +300 or +400 bsp would be preferable, given the risk.

Decide for yourself.

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Re: On Leverage

Post by longinvest » Fri Feb 22, 2019 7:55 am

grayfox wrote:
Fri Feb 22, 2019 7:45 am
But the 64 dollar question is: What is the spread TODAY? If I borrow at mortgage rates and invest in Wellesley Income, what is the spread?
As I've explained earlier in this thread, the mortgage leverages the real estate investment, not the portfolio.

It would be more appropriate to discuss the spread between margin rates and Wellesley Income.

Note that I personally agree with the warning on our wiki's leverage page. I'm allergic to debt.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

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grayfox
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Re: On Leverage

Post by grayfox » Fri Feb 22, 2019 9:08 am

longinvest wrote:
Fri Feb 22, 2019 7:55 am
grayfox wrote:
Fri Feb 22, 2019 7:45 am
But the 64 dollar question is: What is the spread TODAY? If I borrow at mortgage rates and invest in Wellesley Income, what is the spread?
As I've explained earlier in this thread, the mortgage leverages the real estate investment, not the portfolio.

It would be more appropriate to discuss the spread between margin rates and Wellesley Income.
OK, I am lookin at The Best Margin Rates for 2019. If you have $100,00 deposited. Schwab and Fidelity are 7.825% Can that be right? That can not work, unless you have some investment that is guaranteed to pay 12%.

The only broker offering low margin rates is Interactive Brokers at 2.91%. (See footnote) The spread with VWINX would be 4.21 - 2.91 = +130 bsp. Still too small a spread, IMO. Plus I would not switch from Fido, Schwab or Vanguard just to get a cheap margin loan.

Leveraging Wellsley, which I estimate at this time at E.R. = 4.21%, would only begin to make sense if the borrowing rate was less than about 1.7%.

Added: Link to Interactive Brokers Interest Schedule showing interest charged on Margin Loans.
0 - 100K 3.8%
100K - 1M 3.4%
1M - 3M 2.9%
3M - 200M 2.7%
Last edited by grayfox on Mon Feb 25, 2019 8:47 am, edited 2 times in total.

longinvest
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Re: On Leverage

Post by longinvest » Fri Feb 22, 2019 9:26 am

grayfox wrote:
Fri Feb 22, 2019 9:08 am
OK, I am lookin at The Best Margin Rates for 2019. If you have $100,00 deposited. Schwab and Fidelity are 7.825% Can that be right? That can not work, unless you have some investment that is guaranteed to pay 12%.
I think that Dave Ramsey knows where to find this kind of investment. 🤣
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Re: On Leverage

Post by HEDGEFUNDIE » Fri Feb 22, 2019 9:48 am

grayfox wrote:
Fri Feb 22, 2019 9:08 am
longinvest wrote:
Fri Feb 22, 2019 7:55 am
grayfox wrote:
Fri Feb 22, 2019 7:45 am
But the 64 dollar question is: What is the spread TODAY? If I borrow at mortgage rates and invest in Wellesley Income, what is the spread?
As I've explained earlier in this thread, the mortgage leverages the real estate investment, not the portfolio.

It would be more appropriate to discuss the spread between margin rates and Wellesley Income.
OK, I am lookin at The Best Margin Rates for 2019. If you have $100,00 deposited. Schwab and Fidelity are 7.825% Can that be right? That can not work, unless you have some investment that is guaranteed to pay 12%.

The only broker offering low margin rates is Interactive Brokers at 2.91%. The spread with VWINX would be 4.21 - 2.91 = +130 bsp. Still too small a spread, IMO. Plus I would not switch from Fido, Schwab or Vanguard just to get a cheap margin loan.

Leveraging Wellsley, which I estimate at this time at E.R. = 4.21%, would only begin to make sense if the borrowing rate was less than about 1.7%.
If you are moving from theory to practical implementation, you should use credit cards as your source of funds, specifically 0% intro APR cards with no balance transfer fees. BankAmericard is one that offers 18 months at 0%. If your credit is good you can borrow low five figures this way, and continually roll the balance over to new cards.

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Ben Mathew
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Re: On Leverage

Post by Ben Mathew » Fri Feb 22, 2019 10:25 am

grayfox wrote:
Sun Feb 17, 2019 7:43 am
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.
Grayfox, I don't think it can be optimal to leverage a balanced portfolio because you are borrowing money at higher interest to invest at a lower interest in the portion that holds bonds. It would be better to leverage only the stock position--take out a smaller loan and invest in 100% stocks.

So instead of:

$100K margin loan invested in 40/60 ($40K in stocks + $60K in bonds)

go with:

$40K margin loan invested in 100/0 ($40K in stocks + $0 in bonds)

alex_686
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Re: On Leverage

Post by alex_686 » Fri Feb 22, 2019 11:33 am

grayfox wrote:
Fri Feb 22, 2019 7:45 am
But the 64 dollar question is: What is the spread TODAY? If I borrow at mortgage rates and invest in Wellesley Income, what is the spread?
So let me touch on a couple of things.

As other people have suggested, Wellesley may not be the best fund for this exercise. It has a hefty slug of bonds, which makes clearing your spread more difficult (narrower spread between bond returns and your borrowing costs) and will make the calculations more complex. You have done about a 1/3 of the calculations necessary.

First, you don't need to know the return of each asset class (stocks, long bonds, your borrowing costs) but the return of your entire portfolio. i.e., the correlation and casual interplay between these 3 asset classes. 2 specific items.

Second, you need to think about volatility drag. If volatility or returns are normal, then you will have a volatility drag of the square root of your portfolio's return. So if your portfolio has a 10% volatility, then you will have a 3% volatility drag. Some things that you need to think through.

If you increase your allocation to equities you increase your spread and volatility drag.

This calculation falls apart during times of stress and crisis. Increase your leverage and you increase your risk of a total wipe out.

Short term borrowing allows you to have a wider spread, but it has higher volatility than using long term lending, like a mortgage.
grayfox wrote:
Fri Feb 22, 2019 7:45 am
The are all kinds of estimates for the expected return of stocks. Dividend discount model, earnings yield, etc. There is no shortage of forecasts. Pick whichever you like. But a lot of forecasts are around 6%. So I'll go with 6.0%.
Some of these models have volatility drag built into them , like CAPE10. Others, like DDM and earnings yield, do not. If you are using CAPE10 and a mortgage you really don't need to worry about volatility drag. If you use DDM and short term borrowing, you do.

Yeah - I know I am throwing a lot at you. But I am pointing out the levers you can play with on your portfolio.

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Re: On Leverage

Post by pezblanco » Fri Feb 22, 2019 6:17 pm

Ben Mathew wrote:
Fri Feb 22, 2019 10:25 am
grayfox wrote:
Sun Feb 17, 2019 7:43 am
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.
Grayfox, I don't think it can be optimal to leverage a balanced portfolio because you are borrowing money at higher interest to invest at a lower interest in the portion that holds bonds. It would be better to leverage only the stock position--take out a smaller loan and invest in 100% stocks.

So instead of:

$100K margin loan invested in 40/60 ($40K in stocks + $60K in bonds)

go with:

$40K margin loan invested in 100/0 ($40K in stocks + $0 in bonds)
This turns out to not be true. There is an optimal ratio of stocks to bonds AND an optimal leverage for that ratio.

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Re: On Leverage

Post by 305pelusa » Fri Feb 22, 2019 6:34 pm

pezblanco wrote:
Fri Feb 22, 2019 6:17 pm
Ben Mathew wrote:
Fri Feb 22, 2019 10:25 am
grayfox wrote:
Sun Feb 17, 2019 7:43 am
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.
Grayfox, I don't think it can be optimal to leverage a balanced portfolio because you are borrowing money at higher interest to invest at a lower interest in the portion that holds bonds. It would be better to leverage only the stock position--take out a smaller loan and invest in 100% stocks.

So instead of:

$100K margin loan invested in 40/60 ($40K in stocks + $60K in bonds)

go with:

$40K margin loan invested in 100/0 ($40K in stocks + $0 in bonds)
This turns out to not be true. There is an optimal ratio of stocks to bonds AND an optimal leverage for that ratio.
I agree with Ben Mathew and would be very very skeptical that a balanced leveraged portfolio could deliver higher compound or average returns than the same leveraged portfolio, fully in stocks. It honestly makes no sense in my mind (but I've been very wrong before haha).

If you say it's true, please show a simple math example proving so.

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Re: On Leverage

Post by HEDGEFUNDIE » Fri Feb 22, 2019 6:40 pm

305pelusa wrote:
Fri Feb 22, 2019 6:34 pm
pezblanco wrote:
Fri Feb 22, 2019 6:17 pm
Ben Mathew wrote:
Fri Feb 22, 2019 10:25 am
grayfox wrote:
Sun Feb 17, 2019 7:43 am
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.
Grayfox, I don't think it can be optimal to leverage a balanced portfolio because you are borrowing money at higher interest to invest at a lower interest in the portion that holds bonds. It would be better to leverage only the stock position--take out a smaller loan and invest in 100% stocks.

So instead of:

$100K margin loan invested in 40/60 ($40K in stocks + $60K in bonds)

go with:

$40K margin loan invested in 100/0 ($40K in stocks + $0 in bonds)
This turns out to not be true. There is an optimal ratio of stocks to bonds AND an optimal leverage for that ratio.
I agree with Ben Mathew and would be very very skeptical that a balanced leveraged portfolio could deliver higher compound or average returns than the same leveraged portfolio, fully in stocks. It honestly makes no sense in my mind (but I've been very wrong before haha).

If you say it's true, please show a simple math example proving so.
A leveraged stock-only strategy will suffer from huge drawndowns during market crashes. If 100% UPRO had existed through the entire financial crisis it would have suffered a 97% drawdown.

A balanced 40/60 portfolio leveraged up 3x would only have lost 49% (similar to the unleveraged S&P 500)

(There is a nice illustration in the first post of my “Excellent Adventure” thread)

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pezblanco
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Re: On Leverage

Post by pezblanco » Fri Feb 22, 2019 6:58 pm

305pelusa wrote:
Fri Feb 22, 2019 6:34 pm
pezblanco wrote:
Fri Feb 22, 2019 6:17 pm
Ben Mathew wrote:
Fri Feb 22, 2019 10:25 am
grayfox wrote:
Sun Feb 17, 2019 7:43 am
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.
Grayfox, I don't think it can be optimal to leverage a balanced portfolio because you are borrowing money at higher interest to invest at a lower interest in the portion that holds bonds. It would be better to leverage only the stock position--take out a smaller loan and invest in 100% stocks.

So instead of:

$100K margin loan invested in 40/60 ($40K in stocks + $60K in bonds)

go with:

$40K margin loan invested in 100/0 ($40K in stocks + $0 in bonds)
This turns out to not be true. There is an optimal ratio of stocks to bonds AND an optimal leverage for that ratio.
I agree with Ben Mathew and would be very very skeptical that a balanced leveraged portfolio could deliver higher compound or average returns than the same leveraged portfolio, fully in stocks. It honestly makes no sense in my mind (but I've been very wrong before haha).

If you say it's true, please show a simple math example proving so.
See my thread on leveraging stock/bond portfolios .... This isn't anything new to me or Hedgefundie. This is well known.

alex_686
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Re: On Leverage

Post by alex_686 » Fri Feb 22, 2019 7:00 pm

305pelusa wrote:
Fri Feb 22, 2019 6:34 pm
I agree with Ben Mathew and would be very very skeptical that a balanced leveraged portfolio could deliver higher compound or average returns than the same leveraged portfolio, fully in stocks. It honestly makes no sense in my mind (but I've been very wrong before haha).

If you say it's true, please show a simple math example proving so.
If you want a simple example, look at the classic bank model 3-6-3. Borrow at 3% (savings accounts), lend at 6% (loans), hit the golf course by 3 pm. 6% - %3 = 3% return. Leverage by 5x, and your 20% equity generates a very nice 15%, before expenses and loan losses.

On a more serious note, I will point to my prior post on Warren Buffet's use of leverage on low volatility stocks, my prior post on volatility drag, and HEDGEFUNDIE's recent post on crisis / large draw downs. Simple math is not going to cut it, but the math is out there. You need to control the volatility of the long portfolio. I don't think Wellesley Income is the answer due to the concave / convex nature of rebalancing going on here, but it is in the right track.

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Re: On Leverage

Post by Ben Mathew » Fri Feb 22, 2019 7:02 pm

pezblanco wrote:
Fri Feb 22, 2019 6:17 pm
Ben Mathew wrote:
Fri Feb 22, 2019 10:25 am
grayfox wrote:
Sun Feb 17, 2019 7:43 am
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.
Grayfox, I don't think it can be optimal to leverage a balanced portfolio because you are borrowing money at higher interest to invest at a lower interest in the portion that holds bonds. It would be better to leverage only the stock position--take out a smaller loan and invest in 100% stocks.

So instead of:

$100K margin loan invested in 40/60 ($40K in stocks + $60K in bonds)

go with:

$40K margin loan invested in 100/0 ($40K in stocks + $0 in bonds)
This turns out to not be true. There is an optimal ratio of stocks to bonds AND an optimal leverage for that ratio.
It's mathematically impossible for the optimal strategy to involve taking out a loan at 4% and investing it at 3%. Whatever strategy you have in mind, just keep dynamically canceling the bonds and the loans that fund it, and you'll have a better strategy. I'm guessing that what you're referring to is an expected rebalancing bonus within the balanced portfolio that reduces its volatility and/or increases its return. You can achieve that position at a lower cost by adjusting the leveraged stock position over time, without actually borrowing to buy the bonds. Your leveraged stock position will change over time (increase when stocks are down, decrease when stocks are up). You'll just be skipping the part where you have to borrow to invest in bonds.

comeinvest
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Re: On Leverage

Post by comeinvest » Fri Feb 22, 2019 7:05 pm

HEDGEFUNDIE wrote:
Fri Feb 22, 2019 6:40 pm
A balanced 40/60 portfolio leveraged up 3x would only have lost 49% (similar to the unleveraged S&P 500)

(There is a nice illustration in the first post of my “Excellent Adventure” thread)
As I pointed out many times, extrapolating the past into the future is IMHO totally meaningless for bond returns. Bond returns can be very precisely forecast using current yields. I believe it makes zero sense to borrow using a mortgage loan while investing in AAA bonds or bond funds, as it results in a loss with almost mathematical certainty. Regardless how sophisticated your financial models and extrapolations, and/or whether you package your bonds within a hybrid fund. Similarly, it makes zero sense if any portion of your portfolio is bonds, as you would be better off cancelling the respective portion of your loan with an equal amount of your bond portfolio. Whether or not it worked in the past is irrelevant. Also, it would only potentially makes sense to leverage a hybrid fund using short term borrowing rates. A mortgage loan is very similar to bonds for the counterparty, and mortgage rates are typically similar or slightly higher than highly rated bonds. Impossible to make money out of this.

Frankly, I believe the only reasonable way to use leverage in the long run is with an equity-only portfolio and a constant, or amortizing, borrowed amount to avoid volatility drag, at a low enough leverage factor that no margin call will occur, sitting out drawdowns until recovery, and hoping that a tail risk event will not happen. Similar to the "mortgage your retirement" or the "diversification over time" model.
The one other alternative that I see is using constant leverage, accepting the volatility drag and high dispersion of returns, and hoping to benefit from higher expected returns which have shown to be highest somewhere between 1.5 x and 2 x leverage.
Last edited by comeinvest on Fri Feb 22, 2019 7:19 pm, edited 2 times in total.

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pezblanco
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Re: On Leverage

Post by pezblanco » Fri Feb 22, 2019 7:10 pm

Ben Mathew wrote:
Fri Feb 22, 2019 7:02 pm
pezblanco wrote:
Fri Feb 22, 2019 6:17 pm
Ben Mathew wrote:
Fri Feb 22, 2019 10:25 am
grayfox wrote:
Sun Feb 17, 2019 7:43 am
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.
Grayfox, I don't think it can be optimal to leverage a balanced portfolio because you are borrowing money at higher interest to invest at a lower interest in the portion that holds bonds. It would be better to leverage only the stock position--take out a smaller loan and invest in 100% stocks.

So instead of:

$100K margin loan invested in 40/60 ($40K in stocks + $60K in bonds)

go with:

$40K margin loan invested in 100/0 ($40K in stocks + $0 in bonds)
This turns out to not be true. There is an optimal ratio of stocks to bonds AND an optimal leverage for that ratio.
It's mathematically impossible for the optimal strategy to involve taking out a loan at 4% and investing it at 3%.

Yes, that would be true. But we're not just doing that. We're leveraging it. If you take out a loan at 4% and invest it in a 3x leveraged scheme on your 3% money, you get 9% - borrowing costs .... depending on those costs, it can be profitable, right?

Whatever strategy you have in mind, just keep dynamically canceling the bonds and the loans that fund it, and you'll have a better strategy. I'm guessing that what you're referring to is an expected rebalancing bonus within the balanced portfolio that reduces its volatility and/or increases its return. You can achieve that position at a lower cost by adjusting the leveraged stock position over time, without actually borrowing to buy the bonds. Your leveraged stock position will change over time (increase when stocks are down, decrease when stocks are up). You'll just be skipping the part where you have to borrow to invest in bonds.

This is intuitive but not the case. You can achieve higher returns by leveraging a 40/60 or a 50/50 stock/bond portfolio than you can by leveraging a 100% stock portfolio. Again, see my thread on leveraging stock/bond portfolios.

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Re: On Leverage

Post by 305pelusa » Fri Feb 22, 2019 7:15 pm

pezblanco wrote:
Fri Feb 22, 2019 7:10 pm
Ben Mathew wrote:
Fri Feb 22, 2019 7:02 pm
pezblanco wrote:
Fri Feb 22, 2019 6:17 pm
Ben Mathew wrote:
Fri Feb 22, 2019 10:25 am
grayfox wrote:
Sun Feb 17, 2019 7:43 am
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.
Grayfox, I don't think it can be optimal to leverage a balanced portfolio because you are borrowing money at higher interest to invest at a lower interest in the portion that holds bonds. It would be better to leverage only the stock position--take out a smaller loan and invest in 100% stocks.

So instead of:

$100K margin loan invested in 40/60 ($40K in stocks + $60K in bonds)

go with:

$40K margin loan invested in 100/0 ($40K in stocks + $0 in bonds)
This turns out to not be true. There is an optimal ratio of stocks to bonds AND an optimal leverage for that ratio.
It's mathematically impossible for the optimal strategy to involve taking out a loan at 4% and investing it at 3%.

Yes, that would be true. But we're not just doing that. We're leveraging it. If you take out a loan at 4% and invest it in a 3x leveraged scheme on your 3% money, you get 9% - borrowing costs .... depending on those costs, it can be profitable, right?

If you set the borrowing cost = loan cost and the loan cost is greater than the returns of the bond, then 3*(bond return) - 2*(loan cost) will never, ever, ever be greater than (bond return)

Whatever strategy you have in mind, just keep dynamically canceling the bonds and the loans that fund it, and you'll have a better strategy. I'm guessing that what you're referring to is an expected rebalancing bonus within the balanced portfolio that reduces its volatility and/or increases its return. You can achieve that position at a lower cost by adjusting the leveraged stock position over time, without actually borrowing to buy the bonds. Your leveraged stock position will change over time (increase when stocks are down, decrease when stocks are up). You'll just be skipping the part where you have to borrow to invest in bonds.

This is intuitive but not the case. You can achieve higher returns by leveraging a 40/60 or a 50/50 stock/bond portfolio than you can by leveraging a 100% stock portfolio. Again, see my thread on leveraging stock/bond portfolios.

What has occurred has almost no bearing in the fundamental returns of the strategy. I flipped a coin 3 times today and got two tails and a head. Are you telling me there's a 2/3rds chance of getting tails with this coin?
Last edited by 305pelusa on Fri Feb 22, 2019 7:19 pm, edited 1 time in total.

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Re: On Leverage

Post by 305pelusa » Fri Feb 22, 2019 7:18 pm

alex_686 wrote:
Fri Feb 22, 2019 7:00 pm
305pelusa wrote:
Fri Feb 22, 2019 6:34 pm
I agree with Ben Mathew and would be very very skeptical that a balanced leveraged portfolio could deliver higher compound or average returns than the same leveraged portfolio, fully in stocks. It honestly makes no sense in my mind (but I've been very wrong before haha).

If you say it's true, please show a simple math example proving so.
If you want a simple example, look at the classic bank model 3-6-3. Borrow at 3% (savings accounts), lend at 6% (loans), hit the golf course by 3 pm. 6% - %3 = 3% return. Leverage by 5x, and your 20% equity generates a very nice 15%, before expenses and loan losses.

On a more serious note, I will point to my prior post on Warren Buffet's use of leverage on low volatility stocks, my prior post on volatility drag, and HEDGEFUNDIE's recent post on crisis / large draw downs. Simple math is not going to cut it, but the math is out there. You need to control the volatility of the long portfolio. I don't think Wellesley Income is the answer due to the concave / convex nature of rebalancing going on here, but it is in the right track.
If you can borrow at cheaper prices than you can get by lending, then yes, clearly it works. Ben and my assumption is that bond returns aren't going to yield more than the cost to borrow money... Because then those people lending money would just skip you and invest in the bond itself.

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Re: On Leverage

Post by pezblanco » Fri Feb 22, 2019 7:22 pm

305pelusa wrote:
Fri Feb 22, 2019 7:15 pm
pezblanco wrote:
Fri Feb 22, 2019 7:10 pm
Ben Mathew wrote:
Fri Feb 22, 2019 7:02 pm
pezblanco wrote:
Fri Feb 22, 2019 6:17 pm
Ben Mathew wrote:
Fri Feb 22, 2019 10:25 am


Grayfox, I don't think it can be optimal to leverage a balanced portfolio because you are borrowing money at higher interest to invest at a lower interest in the portion that holds bonds. It would be better to leverage only the stock position--take out a smaller loan and invest in 100% stocks.

So instead of:

$100K margin loan invested in 40/60 ($40K in stocks + $60K in bonds)

go with:

$40K margin loan invested in 100/0 ($40K in stocks + $0 in bonds)
This turns out to not be true. There is an optimal ratio of stocks to bonds AND an optimal leverage for that ratio.
It's mathematically impossible for the optimal strategy to involve taking out a loan at 4% and investing it at 3%.

Yes, that would be true. But we're not just doing that. We're leveraging it. If you take out a loan at 4% and invest it in a 3x leveraged scheme on your 3% money, you get 9% - borrowing costs .... depending on those costs, it can be profitable, right?

If you set the borrowing cost = loan cost and the loan cost is greater than the returns of the bond, then 3*(bond return) - 2*(loan cost) will never, ever, ever be greater than (bond return)

Whatever strategy you have in mind, just keep dynamically canceling the bonds and the loans that fund it, and you'll have a better strategy. I'm guessing that what you're referring to is an expected rebalancing bonus within the balanced portfolio that reduces its volatility and/or increases its return. You can achieve that position at a lower cost by adjusting the leveraged stock position over time, without actually borrowing to buy the bonds. Your leveraged stock position will change over time (increase when stocks are down, decrease when stocks are up). You'll just be skipping the part where you have to borrow to invest in bonds.

This is intuitive but not the case. You can achieve higher returns by leveraging a 40/60 or a 50/50 stock/bond portfolio than you can by leveraging a 100% stock portfolio. Again, see my thread on leveraging stock/bond portfolios.

What has occurred has almost no bearing in the fundamental returns of the strategy. I flipped a coin 3 times today and got two tails and a head. Are you telling me there's a 2/3rds chance of getting tails with this coin?
Well that would be the Maximum Likelihood Estimate. :D

Anyway, I think I did misspeak. I originally told Ben that he was incorrect and that leveraging stock/bond portfolios are better than just leveraging stock portfolios. He then posited a scenario where borrowing rate was greater than the bond rate .... I missed that and he is correct in the scenario. However this is not the usual leveraging scenario ... we borrow at short term bond rates and invest in long term bond rates ..... I hope that corrects my error to everyone's satisfaction ... If not, I'll do some other sort of pennance.

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Re: On Leverage

Post by grayfox » Fri Feb 22, 2019 8:04 pm

Ben Mathew wrote:
Fri Feb 22, 2019 7:02 pm
pezblanco wrote:
Fri Feb 22, 2019 6:17 pm
Ben Mathew wrote:
Fri Feb 22, 2019 10:25 am
grayfox wrote:
Sun Feb 17, 2019 7:43 am
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.
Grayfox, I don't think it can be optimal to leverage a balanced portfolio because you are borrowing money at higher interest to invest at a lower interest in the portion that holds bonds. It would be better to leverage only the stock position--take out a smaller loan and invest in 100% stocks.

So instead of:

$100K margin loan invested in 40/60 ($40K in stocks + $60K in bonds)

go with:

$40K margin loan invested in 100/0 ($40K in stocks + $0 in bonds)
This turns out to not be true. There is an optimal ratio of stocks to bonds AND an optimal leverage for that ratio.
It's mathematically impossible for the optimal strategy to involve taking out a loan at 4% and investing it at 3%. Whatever strategy you have in mind, just keep dynamically canceling the bonds and the loans that fund it, and you'll have a better strategy. I'm guessing that what you're referring to is an expected rebalancing bonus within the balanced portfolio that reduces its volatility and/or increases its return. You can achieve that position at a lower cost by adjusting the leveraged stock position over time, without actually borrowing to buy the bonds. Your leveraged stock position will change over time (increase when stocks are down, decrease when stocks are up). You'll just be skipping the part where you have to borrow to invest in bonds.
Yes, it doesn't seem to make sense to borrow at 4% and invest in a portfolio that holds some bonds yielding only 3%. It sounds wrong. It is certainly counter-intuitive.

Yet, it is actually a theoretical result of Modern Portfolio Theory. In MPT, the portfolio with the highest Sharpe Ratio is the Tangency Portfolio TP which lies on the line tangent to the Efficient Frontier EF drawn from the risk-free rate R.f. The risk-free rate is defined as the rate of return for the asset with zero variance over the holding period. See chart.

Image

The tangent line is called the Capital Allocation Line CAL. The idea is that you choose some mix of TP and risk-free asset based on your risk preference. Anywhere from 0% to 100% TP, and then beyond 100% TP if you borrow at R.f., i.e. leverage.

:!: As far as I know, there's no such restriction that the optimum portfolio only include assets with return greater than R.f. In fact, the Tangency Portfolio might include some amount of zero return assets, e.g. gold, if that is optimum portfolio. In theory, even negative return assets could be in TP.

This is the theory, at least. But you're right, it doesn't seem to make sense. I don't know if it actually works out that way or not in practice.

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Re: On Leverage

Post by Ben Mathew » Fri Feb 22, 2019 10:14 pm

grayfox wrote:
Fri Feb 22, 2019 8:04 pm
Yes, it doesn't seem to make sense to borrow at 4% and invest in a portfolio that holds some bonds yielding only 3%. It sounds wrong. It is certainly counter-intuitive.

Yet, it is actually a theoretical result of Modern Portfolio Theory. In MPT, the portfolio with the highest Sharpe Ratio is the Tangency Portfolio TP which lies on the line tangent to the Efficient Frontier EF drawn from the risk-free rate R.f. The risk-free rate is defined as the rate of return for the asset with zero variance over the holding period.
If you can borrow and invest at the same risk free rate, say 3%, then a portfolio where you are effectively borrow at 3% and lend at 3% can be efficient. (It just washes out.) But when you borrow at a higher rate than you can invest in, borrowing at the high rate and investing at a low rate will get you an inefficient portfolio. The simple fact that you can improve the portfolio by getting rid of both the bonds and the loans that fund them to get a better portfolio with the same risk, but higher return, shows that such a portfolio will not be on the efficient frontier.
grayfox wrote:
Fri Feb 22, 2019 8:04 pm
As far as I know, there's no such restriction that the optimum portfolio only include assets with return greater than R.f. In fact, the Tangency Portfolio might include some amount of zero return assets, e.g. gold, if that is optimum portfolio. In theory, even negative return assets could be in TP.

This is the theory, at least. But you're right, it doesn't seem to make sense. I don't know if it actually works out that way or not in practice.
You are right that there is no restriction that the optimum portfolio only includes assets with return greater than the risk free rate. It can even include assets with negative returns. But these assets will still have to contribute to the portfolio by way of risk reduction. E.g., a put option on a stock index will generally have a negative expected return, but it still contributes by reducing the risk of the portfolio. In general there will be an infinite number of ways to decompose efficient portfolios into a group of assets, some of which will have negative expected returns.

But taking out margin loans to buy lower yielding bonds won't fall into this category of acceptable negative return assets, because while the expected return is negative, it does not contribute to reducing the overall risk of the portfolio.

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Re: On Leverage

Post by 305pelusa » Sat Feb 23, 2019 12:57 am

pezblanco wrote:
Fri Feb 22, 2019 7:22 pm
305pelusa wrote:
Fri Feb 22, 2019 7:15 pm
pezblanco wrote:
Fri Feb 22, 2019 7:10 pm
Ben Mathew wrote:
Fri Feb 22, 2019 7:02 pm
pezblanco wrote:
Fri Feb 22, 2019 6:17 pm


This turns out to not be true. There is an optimal ratio of stocks to bonds AND an optimal leverage for that ratio.
It's mathematically impossible for the optimal strategy to involve taking out a loan at 4% and investing it at 3%.

Yes, that would be true. But we're not just doing that. We're leveraging it. If you take out a loan at 4% and invest it in a 3x leveraged scheme on your 3% money, you get 9% - borrowing costs .... depending on those costs, it can be profitable, right?

If you set the borrowing cost = loan cost and the loan cost is greater than the returns of the bond, then 3*(bond return) - 2*(loan cost) will never, ever, ever be greater than (bond return)

Whatever strategy you have in mind, just keep dynamically canceling the bonds and the loans that fund it, and you'll have a better strategy. I'm guessing that what you're referring to is an expected rebalancing bonus within the balanced portfolio that reduces its volatility and/or increases its return. You can achieve that position at a lower cost by adjusting the leveraged stock position over time, without actually borrowing to buy the bonds. Your leveraged stock position will change over time (increase when stocks are down, decrease when stocks are up). You'll just be skipping the part where you have to borrow to invest in bonds.

This is intuitive but not the case. You can achieve higher returns by leveraging a 40/60 or a 50/50 stock/bond portfolio than you can by leveraging a 100% stock portfolio. Again, see my thread on leveraging stock/bond portfolios.

What has occurred has almost no bearing in the fundamental returns of the strategy. I flipped a coin 3 times today and got two tails and a head. Are you telling me there's a 2/3rds chance of getting tails with this coin?
Well that would be the Maximum Likelihood Estimate. :D

Anyway, I think I did misspeak. I originally told Ben that he was incorrect and that leveraging stock/bond portfolios are better than just leveraging stock portfolios. He then posited a scenario where borrowing rate was greater than the bond rate .... I missed that and he is correct in the scenario. However this is not the usual leveraging scenario ... we borrow at short term bond rates and invest in long term bond rates ..... I hope that corrects my error to everyone's satisfaction ... If not, I'll do some other sort of pennance.
I see. Still considering that:
1) Borrowing still has to be at a higher rate than short term bond rates (again, otherwise, the lenders would just invest in the short term bonds themselves). I don't know how much higher and I'm sure it depends on the product (no clue the equivalent borrowing cost of those 3x ETFs). But I imagine a fair amount higher.
And
2) The premium (spread) from short to long term bonds is a minuscule ~0.5%. And you pay taxes on that (unless you leverage in tax-advantaged I suppose).

Allow me to remain extremely skeptical that any portfolio would benefit from borrowing at short term rates and investing in long term treasuries (I believe that's your example) at the moment.

I'm with Ben on this one. I don't think borrowing money to lend it will generally make a profit. And if the profit would come from extending the maturity, our current time is about the worst one (except for an inverted curve I guess) where I can imagine it making any sense.

Just my 2 cents

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Re: On Leverage

Post by HEDGEFUNDIE » Sat Feb 23, 2019 1:03 am

305pelusa wrote:
Sat Feb 23, 2019 12:57 am

I see. Still considering that:
1) Borrowing still has to be at a higher rate than short term bond rates (again, otherwise, the lenders would just invest in the short term bonds themselves). I don't know how much higher and I'm sure it depends on the product (no clue the equivalent borrowing cost of those 3x ETFs). But I imagine a fair amount higher.
Not necessarily true. See viewtopic.php?p=4397820#p4397820

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Re: On Leverage

Post by 305pelusa » Sat Feb 23, 2019 1:11 am

grayfox wrote:
Fri Feb 22, 2019 8:04 pm
Ben Mathew wrote:
Fri Feb 22, 2019 7:02 pm
pezblanco wrote:
Fri Feb 22, 2019 6:17 pm
Ben Mathew wrote:
Fri Feb 22, 2019 10:25 am
grayfox wrote:
Sun Feb 17, 2019 7:43 am
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.
Grayfox, I don't think it can be optimal to leverage a balanced portfolio because you are borrowing money at higher interest to invest at a lower interest in the portion that holds bonds. It would be better to leverage only the stock position--take out a smaller loan and invest in 100% stocks.

So instead of:

$100K margin loan invested in 40/60 ($40K in stocks + $60K in bonds)

go with:

$40K margin loan invested in 100/0 ($40K in stocks + $0 in bonds)
This turns out to not be true. There is an optimal ratio of stocks to bonds AND an optimal leverage for that ratio.
It's mathematically impossible for the optimal strategy to involve taking out a loan at 4% and investing it at 3%. Whatever strategy you have in mind, just keep dynamically canceling the bonds and the loans that fund it, and you'll have a better strategy. I'm guessing that what you're referring to is an expected rebalancing bonus within the balanced portfolio that reduces its volatility and/or increases its return. You can achieve that position at a lower cost by adjusting the leveraged stock position over time, without actually borrowing to buy the bonds. Your leveraged stock position will change over time (increase when stocks are down, decrease when stocks are up). You'll just be skipping the part where you have to borrow to invest in bonds.
Yes, it doesn't seem to make sense to borrow at 4% and invest in a portfolio that holds some bonds yielding only 3%. It sounds wrong. It is certainly counter-intuitive.

Yet, it is actually a theoretical result of Modern Portfolio Theory.
Wait no. Please listen to PezBlanco. Though he is a proponent of borrowing to invest in debt, even he realizes that scenario makes no sense. There has to be some premium. If you borrow at X rate, your investment must return a little more than X long term to work. Borrowing at short term rates and investing at long term rates still technically meets that. Borrowing at 4% and investing at anything under that does not.

I'm not sure you can just grab a portfolio that has a high (or even highest) Sharpe Ratio, and then just leverage that up. Im not sure that necessarily works. If it did, one could:

1) Grab portfolio with highest Sharpe Ratio (say that's a mix of some stocks and bonds).
2) Leverage it until it meets the volatility of 100% stocks.
3) Since the Sharpe was higher, the return must be higher than 100% stocks.

That only works if leverage does not change the Sharpe Ratio. If it did (and fundamentally, it has to... otherwise the above 3 steps are a free lunch), then nothing ensures that leveraging an "optimal" portfolio makes it better than some other leveraged, previously "not-so-optimal" portfolio.

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Re: On Leverage

Post by HEDGEFUNDIE » Sat Feb 23, 2019 1:22 am

305pelusa wrote:
Sat Feb 23, 2019 1:11 am
I'm not sure you can just grab a portfolio that has a high (or even highest) Sharpe Ratio, and then just leverage that up. Im not sure that necessarily works. If it did, one could:

1) Grab portfolio with highest Sharpe Ratio (say that's a mix of some stocks and bonds).
2) Leverage it until it meets the volatility of 100% stocks.
3) Since the Sharpe was higher, the return must be higher than 100% stocks.
This is exactly what modern portfolio theory tells you. You get to the Capital Allocation Line, the slope of which represents the highest Sharpe Ratio. And then when you lever up, you move up along the line (up and away from the efficient frontier).

Note that moving up along the line with leverage does not mean the Sharpe Ratio increases. It stays the same, as you are on the same line, with the same slope. You are increasing return but also increasing risk at the same ratio. So no free lunch.

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Re: On Leverage

Post by 305pelusa » Sat Feb 23, 2019 1:33 am

HEDGEFUNDIE wrote:
Sat Feb 23, 2019 1:03 am
305pelusa wrote:
Sat Feb 23, 2019 12:57 am

I see. Still considering that:
1) Borrowing still has to be at a higher rate than short term bond rates (again, otherwise, the lenders would just invest in the short term bonds themselves). I don't know how much higher and I'm sure it depends on the product (no clue the equivalent borrowing cost of those 3x ETFs). But I imagine a fair amount higher.
Not necessarily true. See viewtopic.php?p=4397820#p4397820
I don't know much about those vehicles; I admit my ignorance. However, tell me if I'm missing something:

From 2011-2012, TLT returned 17.25 while TMF returned 45.05. AFAIK, the expense that year was 17.25*3-45.05=6.7%.
From 2014-2015, TLT returned 11.81 while TMF returned 30.48. AFAIK, the expense that year was 11.81*3-30.48=4.95%.

I didn't really bother too look at any more years. I tried to pick years with very few losses to ensure there's very minimal volatility drag incorporated in that loss.
I'm sure that expense number will include regular expenses to handle the fund itself as well as the borrowing cost to leverage.

Are you sure the numbers you linked me to don't refer simply to the management fees of the fund? And that the true cost of actually leveraging the product itself can only be somewhat deducted by noticing how much it trails it's benchmark, proportional-wise? So the cost to borrow for those costs would be the numbers I derived, minus the numbers you linked me to?

Again, don't know anything about them. Just trying to apply some common sense. You know more about this than me.
Last edited by 305pelusa on Sat Feb 23, 2019 1:35 am, edited 1 time in total.

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Re: On Leverage

Post by 305pelusa » Sat Feb 23, 2019 1:34 am

HEDGEFUNDIE wrote:
Sat Feb 23, 2019 1:22 am
305pelusa wrote:
Sat Feb 23, 2019 1:11 am
I'm not sure you can just grab a portfolio that has a high (or even highest) Sharpe Ratio, and then just leverage that up. Im not sure that necessarily works. If it did, one could:

1) Grab portfolio with highest Sharpe Ratio (say that's a mix of some stocks and bonds).
2) Leverage it until it meets the volatility of 100% stocks.
3) Since the Sharpe was higher, the return must be higher than 100% stocks.
This is exactly what modern portfolio theory tells you. You get to the Capital Allocation Line, the slope of which represents the highest Sharpe Ratio. And then when you lever up, you move up along the line (up and away from the efficient frontier).

Note that moving up along the line with leverage does not mean the Sharpe Ratio increases. It stays the same, as you are on the same line, with the same slope. You are increasing return but also increasing risk at the same ratio. So no free lunch.
All right fair enough. I guess I don't know much about the theory then haha.

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Re: On Leverage

Post by HEDGEFUNDIE » Sat Feb 23, 2019 1:48 am

305pelusa wrote:
Sat Feb 23, 2019 1:33 am
HEDGEFUNDIE wrote:
Sat Feb 23, 2019 1:03 am
305pelusa wrote:
Sat Feb 23, 2019 12:57 am

I see. Still considering that:
1) Borrowing still has to be at a higher rate than short term bond rates (again, otherwise, the lenders would just invest in the short term bonds themselves). I don't know how much higher and I'm sure it depends on the product (no clue the equivalent borrowing cost of those 3x ETFs). But I imagine a fair amount higher.
Not necessarily true. See viewtopic.php?p=4397820#p4397820
I don't know much about those vehicles; I admit my ignorance. However, tell me if I'm missing something:

From 2011-2012, TLT returned 17.25 while TMF returned 45.05. AFAIK, the expense that year was 17.25*3-45.05=6.7%.
From 2014-2015, TLT returned 11.81 while TMF returned 30.48. AFAIK, the expense that year was 11.81*3-30.48=4.95%.

I didn't really bother too look at any more years. I tried to pick years with very few losses to ensure there's very minimal volatility drag incorporated in that loss.
I'm sure that expense number will include regular expenses to handle the fund itself as well as the borrowing cost to leverage.

Are you sure the numbers you linked me to don't refer simply to the management fees of the fund? And that the true cost of actually leveraging the product itself can only be somewhat deducted by noticing how much it trails it's benchmark, proportional-wise? So the cost to borrow for those costs would be the numbers I derived, minus the numbers you linked me to?

Again, don't know anything about them. Just trying to apply some common sense. You know more about this than me.
The "expense" that you calculated actually includes a whole bunch of things, but mostly it's the "volatility drag" of a daily-leverage-reset ETF which has nothing to do with the cost of borrowing. There are 700 posts in my other thread explaining this if you are interested. :wink:

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Re: On Leverage

Post by grayfox » Sat Feb 23, 2019 7:58 am

305pelusa wrote:
Sat Feb 23, 2019 1:11 am
grayfox wrote:
Fri Feb 22, 2019 8:04 pm

Yes, it doesn't seem to make sense to borrow at 4% and invest in a portfolio that holds some bonds yielding only 3%. It sounds wrong. It is certainly counter-intuitive.

Yet, it is actually a theoretical result of Modern Portfolio Theory.
Wait no. Please listen to PezBlanco. Though he is a proponent of borrowing to invest in debt, even he realizes that scenario makes no sense. There has to be some premium. If you borrow at X rate, your investment must return a little more than X long term to work. Borrowing at short term rates and investing at long term rates still technically meets that. Borrowing at 4% and investing at anything under that does not.

I'm not sure you can just grab a portfolio that has a high (or even highest) Sharpe Ratio, and then just leverage that up. Im not sure that necessarily works. If it did, one could:

1) Grab portfolio with highest Sharpe Ratio (say that's a mix of some stocks and bonds).
2) Leverage it until it meets the volatility of 100% stocks.
3) Since the Sharpe was higher, the return must be higher than 100% stocks.

That only works if leverage does not change the Sharpe Ratio. If it did (and fundamentally, it has to... otherwise the above 3 steps are a free lunch), then nothing ensures that leveraging an "optimal" portfolio makes it better than some other leveraged, previously "not-so-optimal" portfolio.
This seems like a conundrum. From common sense, it should not be worthwhile borrowing at 4% and putting 60% of that into bonds yielding 3%. It makes no sense.

In the simulation, one thing I notice is that the Sharpe ratio did not stay the same 0.91, but actually went down with more leverage.

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
Maybe the MPT result only holds if you borrow at the risk-free rate. If you borrow at at higher rate, it doesn't work.

This could be one of those rare cases where theory and practice are different. Like LTCM, the theory said they would make billions, instead they lost trillions. Yogi was right. :D

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Re: On Leverage

Post by alex_686 » Sat Feb 23, 2019 8:23 am

grayfox wrote:
Sat Feb 23, 2019 7:58 am
In the simulation, one thing I notice is that the Sharpe ratio did not stay the same 0.91, but actually went down with more leverage.
...
Maybe the MPT result only holds if you borrow at the risk-free rate. If you borrow at at higher rate, it doesn't work.
This should make intuitive sense. The Sharpe Ratio is basically "return per unit of risk taken". Leverage up the portfolio, leverage up the risk. The Sharpe Ratio must change. Also, MPT makes some simplifying assumptions that risk and return are linear and they are not, in particular in times of crisis.

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Re: On Leverage

Post by grayfox » Sat Feb 23, 2019 8:41 am

This reminds of the time when our friend Larry promoted the Commodities fund PCRIX. A couple of years later, it was way down. If you invested in it, you would have lost a bunch of money. Someone posted how badly it had done. But then Larry said, run the numbers. If you had added a small amount to a portfolio, it actually improved the portfolio risk/return over that period.

He was right. :o PCRIX was very volatile, and somehow going up and down countered the down and up in stocks and even though overall the whole period PCRIX was showed losses, the whole portfolio was better.

The lesson was that it was the whole portfolio that mattered, rather than the individual components.

I don't know if that applies here. But if you look at Wellesley as a whole portfolio, it had good return with low volatility. So a high Sharpe ratio. Levering up the whole portfolio works great. As long as you don't look inside. Once you look inside and you see low return bonds and realize it can't work, it stops working.

Don't look inside the box! It works as long as you believe it works. It stops working when you stop believing.

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Re: On Leverage

Post by longinvest » Sat Feb 23, 2019 9:34 am

grayfox wrote:
Sat Feb 23, 2019 8:41 am
This reminds of the time when our friend Larry promoted the Commodities fund PCRIX. A couple of years later, it was way down. If you invested in it, you would have lost a bunch of money. Someone posted how badly it had done. But then Larry said, run the numbers. If you had added a small amount to a portfolio, it actually improved the portfolio risk/return over that period.

He was right. PCRIX was very volatile, and somehow it going up and down countered the down and up in stocks and even though overall the whole period PCRIX was showed losses, the whole portfolio was better.
Dear Grayfox,

There's no need to propagate myths. Swedroe was wrong all along.

Adding even as little as 5% PCRIX to a Three-Fund Portfolio in 2008, when he was still promoting CCFs as much as he does factors these days, had a negative impact on returns while increasing volatility and decreasing Sharpe ratio.

You don't have to believe me. You just have to check the facts. Here's a link to a Portfolio Visualizer backtest:

https://www.portfoliovisualizer.com/bac ... ation4_2=5

Best regards,

longinvest
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Re: On Leverage

Post by grayfox » Sun Feb 24, 2019 6:51 am

longinvest wrote:
Sat Feb 23, 2019 9:34 am
grayfox wrote:
Sat Feb 23, 2019 8:41 am
This reminds of the time when our friend Larry promoted the Commodities fund PCRIX. A couple of years later, it was way down. If you invested in it, you would have lost a bunch of money. Someone posted how badly it had done. But then Larry said, run the numbers. If you had added a small amount to a portfolio, it actually improved the portfolio risk/return over that period.

He was right. PCRIX was very volatile, and somehow it going up and down countered the down and up in stocks and even though overall the whole period PCRIX was showed losses, the whole portfolio was better.
Dear Grayfox,

There's no need to propagate myths. Swedroe was wrong all along.

Adding even as little as 5% PCRIX to a Three-Fund Portfolio in 2008, when he was still promoting CCFs as much as he does factors these days, had a negative impact on returns while increasing volatility and decreasing Sharpe ratio.

You don't have to believe me. You just have to check the facts. Here's a link to a Portfolio Visualizer backtest:

https://www.portfoliovisualizer.com/bac ... ation4_2=5

Best regards,

longinvest
That's today in 2019. But when Larry made that statement,which was probably about 2009, he was correct. At least looking backwards. Change the dates to 2001-2009. Also make Portfolio #3 100% PCRIX to show how badly it recently had fallen.

Unfortunately, it didn't work going forward from 2009. But all backtest results depend on the endpoints anyway.

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Re: On Leverage

Post by grayfox » Sun Feb 24, 2019 8:00 am

According to MPT, based on your risk preference, you would lever up or down the portfolio with the highest Sharpe Ratio.

In an earlier post, I ran various equity and bond asset classes though portfoliovisualizer. The stocks varied from SR = .27 for Emerging Markets to SR = .49 for Large-Cap Value. The bonds generally had higher SR, e.g. .71 for Total US Bonds. The were a couple of outliers like -0.55 for Corporate bonds since 2003 (probably too short a period to be meaningful) and 1.02 for USD-Hedged Global bonds since 1999. How did that come out so high?

Should there be more stock, more bonds? If you are going by Sharpe Ratio, it looks like more bonds. Then I listed some balanced funds like 60/40 and 40/60 and that's how I got to Wellesley which had SR = 0.91 since 1985. That's pretty high and for a long time.

I thought I would just limit it now to Index Funds since there is a lot of chatter about leveraging a portfolio of S&P500 and 20-year Treasuries. Vanguard funds would be VFINX and VUSTX, which has a long history going back to Jun-1986. Which mix of VFINX/VUSTX had the highest Sharpe Ratio. Without further ado, here it is:

Jun-1986 to Jan 2019

Code: Select all

VFINX/VUSTX     Initial Final Balance   CAGR    Stdev   Best    Worst   Max. Drawdown   Sharpe Ratio
100/0           $10,000 $218,614        9.90%   14.91%  37.45%  -37.02% -50.97%         0.50       <-- highest return  
90/10           $10,000 $216,631        9.87%   13.36%  36.71%  -31.07% -45.27%         0.54    
80/20           $10,000 $211,037        9.78%   11.92%  35.98%  -25.11% -39.38%         0.59    
70/30           $10,000 $202,357        9.64%   10.63%  35.24%  -19.16% -33.27%         0.63    
60/40           $10,000 $191,155        9.45%   9.52%   34.50%  -13.21% -26.96%         0.67    
50/50           $10,000 $178,012        9.21%   8.65%   33.77%  -7.25%  -20.51%         0.71    
45/55           $10,000 $170,892        9.08%   8.32%   33.40%  -4.28%  -17.53%         0.72     <-- highest SR
40/60           $10,000 $163,498        8.93%   8.09%   33.03%  -3.75%  -14.52%         0.72     <-- highest SR
35/65           $10,000 $155,898        8.77%   7.94%   32.67%  -4.16%  -12.47%         0.71
30/70           $10,000 $148,154        8.60%   7.90%   32.30%  -4.57%  -12.03%         0.69      <-- lowest Std Dev
20/80           $10,000 $132,471        8.23%   8.11%   31.56%  -5.40%  -11.15%         0.64
10/90           $10,000 $116,886        7.82%   8.70%   30.83%  -8.51%  -12.43%         0.55
0/100           $10,000 $101,765        7.36%   9.62%   30.09%  -13.03% -16.68%         0.47
Over the period examined, It looks like 40 to 45 percent stocks was the sweet spot, as far as Sharpe Ratio. It didn't have the highest return, which was 100% VFINX. It didn't have the lowest Std Dev, which was 30/70. It didn't have the least Max DD which was 20/80. But it had the best combination of risk and return, according to Sharpe.

Still no combination of VFINX and VUSTX had a Sharpe Ratio as high as Wellesley. Or USD-Hedged Global bonds.

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Re: On Leverage

Post by longinvest » Sun Feb 24, 2019 8:14 am

grayfox wrote:
Sun Feb 24, 2019 6:51 am
longinvest wrote:
Sat Feb 23, 2019 9:34 am
grayfox wrote:
Sat Feb 23, 2019 8:41 am
This reminds of the time when our friend Larry promoted the Commodities fund PCRIX. A couple of years later, it was way down. If you invested in it, you would have lost a bunch of money. Someone posted how badly it had done. But then Larry said, run the numbers. If you had added a small amount to a portfolio, it actually improved the portfolio risk/return over that period.

He was right. PCRIX was very volatile, and somehow it going up and down countered the down and up in stocks and even though overall the whole period PCRIX was showed losses, the whole portfolio was better.
Dear Grayfox,

There's no need to propagate myths. Swedroe was wrong all along.

Adding even as little as 5% PCRIX to a Three-Fund Portfolio in 2008, when he was still promoting CCFs as much as he does factors these days, had a negative impact on returns while increasing volatility and decreasing Sharpe ratio.

You don't have to believe me. You just have to check the facts. Here's a link to a Portfolio Visualizer backtest:

https://www.portfoliovisualizer.com/bac ... ation4_2=5

Best regards,

longinvest
That's today in 2019. But when Larry made that statement,which was probably about 2009, he was correct. At least looking backwards. Change the dates to 2001-2009. Also make Portfolio #3 100% PCRIX to show how badly it recently had fallen.

Unfortunately, it didn't work going forward from 2009. But all backtest results depend on the endpoints anyway.
Dear Grayfox,

I chose early 2008 as start point because The Great Commodities Debate between Rick Ferri and Larry Swedroe took place on February 11 and 14, 2008: Best regards,

longinvest
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Re: On Leverage

Post by grayfox » Sun Feb 24, 2019 12:18 pm

I notice that the portfoliovisualizer backtest for VFINX/VUSTX goes back to June 1986. It reminded me of something. Back about that same time, I was at work one day when two of my co-workers got into a huge debate about this very topic, using mortgage to invest in the stock market. The first guy had a mortgage but was investing in stocks. The second guy said he would not invest in the stock market until he paid off his mortgage.

First guy said if stocks return more than he pays in mortgage interest, he will come out ahead. Second guy didn't believe it and said impossible. The debate raged on. Each came up with example and counter-example. This was long before you could look up everything on the internet. Basically you only had a whiteboard and a calculator. Only a few people even had Lotus 1,2,3 spreadsheet at that time. Very little historical market data was available to the average investor. Maybe you had Random Walk Down Wall Street which had a few tables.

It is funny that the debate is still going on. I still don't know the answer. But I decided to look up what the numbers would have looked like back then. If we had data back then, would it have seemed like a good idea to leverage a 40/60 VFINX/VUSTX? Let's find out!

I looked up most of the numbers on FRED and did some back-of-the-envelope calculations.

Code: Select all

			Jun-1986
1M LIBOR		7.12500%
1M LIBOR+1%		8.125%
30 YR FIXED MORTGAGE	10.38%
20-YR TREAS		7.69%
CPI CHANGE Y-O-Y	3.54%
INFLATION EXP		3.54%
CAPE			13.89
1/CAPE			7.20%
VFINX E.R.		10.74%
VUSTX E.R.		7.69%
40/60 VFINX/VUSTX	8.91%
SPREAD (bsp)		78.48
First of all, the 30-Year Fixed mortgage was 10.38% and the 20-Year Treasury was yielding 7.69%.
The previous year had +3.54% CPI inflation, which I am calling the inflation expectations. They didn't start reporting inflation expectations until the 2000's.
CAPE was 13.89, so I am estimating that the S&P500 would return 10.74% before inflation.
The 40/60 portfolio had Expected Return = 8.91% before inflation.

This is less than the 30-Year mortgage rate of 10.38%. So I would have said, forget about mortgaging the house to invest in 40/60 in June 1986. :thumbsdown

What about borrowing at 1-Month LIBOR + 1% = 8.125% ?
That gives you a spread of 78 basis points. I would have passed on that, also. :thumbsdown

What was the actually result with 40/60 VFINX/VUSTX?

Jan 1987 - Jan 2019

Code: Select all

Portfolio	Initial	Final Balance	CAGR	Stdev	Best	Worst	Max. Drawdown	Sharpe Ratio
40/60		$10,000	$156,802 	8.96% 	7.99%	33.03%	-3.75%	-14.52% 	0.74
Very close to what a forecast using CAPE, last-year's inflation rate and 20-year Treasury yield would have predicted. :thumbsup

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Re: On Leverage

Post by alex_686 » Sun Feb 24, 2019 12:36 pm

grayfox wrote:
Sun Feb 24, 2019 12:18 pm
It is funny that the debate is still going on. I still don't know the answer. But I decided to look up what the numbers would have looked like back then.
So, while doing my weekend reading, I was remained of 2 things.

First, mortgages are exposed to different interest rate factors than long bonds, cash, and equity returns. So you get some modest diversification of risk factors with a mortgage.

Second - and more importantly - that leverage increases risk/return lineally, but it increases volatility drag exponentially. So while modest leverage can increase your Sharpe ratio, at a certain level that low volatility drag will grow faster than the extra risk / returns.

A last point is that your model does capture normal markets decently, but there is a real "tail risk" - black swans that come in and blow everything up.

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Re: On Leverage

Post by grayfox » Mon Feb 25, 2019 7:26 am

As long as I have a simple methodology for accepting/rejecting leverage trades, I might as well apply to to the current situation. I'll do the same thing I did for June-1986 (when the portviz data begins): estimate the portfolio return and see what kind of profit I would have over two possible borrowing costs: 30-Year Fixed Mortgage and 1-Month LIBOR + 1%. I show Jan-2019 next to Jun-1986 for comparison:

Code: Select all

			Jan-2019	Jun-1986
			
1M LIBOR		2.50713%	7.12500%
3M LIBOR		2.79388%	7.12500%
1M LIBOR + 1%		3.507%		8.125%
			
30 YR FIXED MORTGAGE	4.51%		10.38%
20-YR TREAS		2.89%		7.69%
CPI CHANGE Y-O-Y	2.13%		3.54%
INFLATION EXP		1.87%		3.54%
			
CAPE			28.70		13.89
1/CAPE			3.48%		7.20%
			
VFINX E.R.		5.35%		10.74%
VUSTX E.R.		2.89%		7.69%
40/60 VFINX/VUSTX	3.88%		8.91%
SPREAD (bsp)		36.86		78.48
Obviously, conditions are completely different in 2019 than in 1986. Back then, interest rates were higher, inflation and inflation expectations were higher, stock values were half what they are today. Portfolio of stocks and bonds had much better expectations.

Way different situation today, but the conclusions are pretty much the same.
First, there is no profit in using 4.51% mortage to leverage a portfolio with 3.88% expected return. Reject that trade. :thumbsdown
Borrowing at 1M LIBOR+1% = 3.5% has a slim margin over the 40/60, +37 basis points. At least it's positive.
But not enough to make up for the risk. Rejected :thumbsdown

My conclusion at this time for leveraging 40/60 portfolio: Fuhgeddaboudit!

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Re: On Leverage

Post by pezblanco » Mon Feb 25, 2019 9:49 am

grayfox wrote:
Mon Feb 25, 2019 7:26 am
As long as I have a simple methodology for accepting/rejecting leverage trades, I might as well apply to to the current situation. I'll do the same thing I did for June-1986 (when the portviz data begins): estimate the portfolio return and see what kind of profit I would have over two possible borrowing costs: 30-Year Fixed Mortgage and 1-Month LIBOR + 1%. I show Jan-2019 next to Jun-1986 for comparison:

Code: Select all

			Jan-2019	Jun-1986
			
1M LIBOR		2.50713%	7.12500%
3M LIBOR		2.79388%	7.12500%
1M LIBOR + 1%		3.507%		8.125%
			
30 YR FIXED MORTGAGE	4.51%		10.38%
20-YR TREAS		2.89%		7.69%
CPI CHANGE Y-O-Y	2.13%		3.54%
INFLATION EXP		1.87%		3.54%
			
CAPE			28.70		13.89
1/CAPE			3.48%		7.20%
			
VFINX E.R.		5.35%		10.74%
VUSTX E.R.		2.89%		7.69%
40/60 VFINX/VUSTX	3.88%		8.91%
SPREAD (bsp)		36.86		78.48
Obviously, conditions are completely different in 2019 than in 1986. Back then, interest rates were higher, inflation and inflation expectations were higher, stock values were half what they are today. Portfolio of stocks and bonds had much better expectations.

Way different situation today, but the conclusions are pretty much the same.
First, there is no profit in using 4.51% mortage to leverage a portfolio with 3.88% expected return. Reject that trade. :thumbsdown
Borrowing at 1M LIBOR+1% = 3.5% has a slim margin over the 40/60, +37 basis points. At least it's positive.
But not enough to make up for the risk. Rejected :thumbsdown

My conclusion at this time for leveraging 40/60 portfolio: Fuhgeddaboudit!
grayfox, the issue really for leverage is always going to be the borrowing rate, right? IB will only give you 1.5% + T-bill for the first 100K (1% + T-bill for sums greater than that), the x leveraged funds have borrowing rates it seems like are something like (x-1)*libor +1, but with their daily rebalancing they suffer quite a bit of volatility drag (maybe another 1.5% to 2% annually?). How about looking at leveraging with options? ... buy long term call options deep in the money (LEAPS). (Yes, I know, this is what Markettimer did in the most famous thread in history on BH ... but it's still a very good idea for getting effective borrow rates quite low. There is even academic research ... see Ayres and Nalebuff) If you're serious about leveraging, this is the next step! :D

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Re: On Leverage

Post by grayfox » Tue Feb 26, 2019 8:14 am

pezblanco wrote:
Mon Feb 25, 2019 9:49 am
grayfox, the issue really for leverage is always going to be the borrowing rate, right? IB will only give you 1.5% + T-bill for the first 100K (1% + T-bill for sums greater than that), the x leveraged funds have borrowing rates it seems like are something like (x-1)*libor +1, but with their daily rebalancing they suffer quite a bit of volatility drag (maybe another 1.5% to 2% annually?).
Interactive Brokers Interest Schedule shows USD Benchmark = 2.400% and the margin rate is
0 - 100K: BM + 1.5%
100K - 1M: BM + 1%
1M - 3M 2.9%: BM + 0.5%
3M - 200M 2.7%: BM + 0.3%

It all boils down to the difference between how much can you borrow at and how much can you invest at. Which I'll call the profit.

After considering this subject for a while, it seems to me one should be able to look at a proposed leverage trade and, using a rule of thumb, decide within 30 seconds if it should be immediately rejected or whether it warrants more detailed analysis. Just ask:

What rate can I borrow at?
What rate can I invest at?
How volatile is the investment?
What is the minimum profit that would make this worthwhile?

If less than some minimum profit, Fuhgeddaboudit.

The minimum profit should depend on how volatile the investment. This is Ferengi Rule 62. The riskier the road, the greater the profit.
E.g. If I could invest in 5% bank CD, I would gladly borrow at 4.9% and leverage 100:1.
But if it was S&P500, I would probably want at least +500 bsp profit to leverage 1.5:1.
40/60, maybe +300 bsp.

Like the banker's 3-6-3 Rule from a previous poster: pay depositors 3%, lend at 6%, on the links by 3PM.
pezblanco wrote:
Mon Feb 25, 2019 9:49 am
How about looking at leveraging with options? ... buy long term call options deep in the money (LEAPS). (Yes, I know, this is what Markettimer did in the most famous thread in history on BH ... but it's still a very good idea for getting effective borrow rates quite low. There is even academic research ... see Ayres and Nalebuff) If you're serious about leveraging, this is the next step! :D
Options and futures look too complicated to understand.

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Re: On Leverage

Post by SovereignInvestor » Tue Feb 26, 2019 8:58 am

Leveraging up and then putting the proceeds in any sort of low risk (especially risk free) bonds is just reckless.  Especially in taxable account where it is horrible for taxes.

The flaw in many analyses here is that yes a blend of stocks and bonds does optimize sharpe...but only of the portfolio using borrowed money.

If we have 100K equity.  And then borrow 50K and are thinking of doing 60/40 stock bond with the borrowed 50K to maximize the sharpe...that is the wrong metric.

The sharpe of the 50K borrowed doesn't matter...Capital is fungible..what matters is the sharpe of the entire portfolio.

So one should keep selling the low risk bonds to deleverage.  Instead of borrowing 50K to have 20K of it in low risk bonds and 30K in equity...just borrow 30K and put it in equity.  Yes the sharpe on the 30K will be lower...but the ENTIRE portfolio of 130K will have better sharpe than if it was 150K and 20K sat in bonds that aren't covering the cost of borrowing.

As far as leverage...using options LEAPS is ideal.  It makes one borrow at the risk free rate since options are collateralized and require margin.

The issue with using ITM Call Leaps to approximate borrowing risk free and buying equities is its not that tax efficient. The best scenario if one profits is they would pay LTCG tax but worse than buying and holding equity underlying if they wanted long term leverage.  Leap calls are essentially being long underlying and long a put so one can do that instead and that is more tax efficient...but theoretically requires borrowing on margin to buy more underlying at rates above risk free....it's more tax efficient though because only the put expires..but if stocks keep rising there's no required tax on the Equity holding. But one must borrow..but if using a put to hedge the risk of margin call is not really there...it's just bad because high cost of borrowing.

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Re: On Leverage

Post by EfficientInvestor » Tue Feb 26, 2019 9:32 am

pezblanco wrote:
Mon Feb 25, 2019 9:49 am
grayfox, the issue really for leverage is always going to be the borrowing rate, right? IB will only give you 1.5% + T-bill for the first 100K (1% + T-bill for sums greater than that), the x leveraged funds have borrowing rates it seems like are something like (x-1)*libor +1, but with their daily rebalancing they suffer quite a bit of volatility drag (maybe another 1.5% to 2% annually?). How about looking at leveraging with options? ... buy long term call options deep in the money (LEAPS). (Yes, I know, this is what Markettimer did in the most famous thread in history on BH ... but it's still a very good idea for getting effective borrow rates quite low. There is even academic research ... see Ayres and Nalebuff) If you're serious about leveraging, this is the next step! :D
Correct me if I'm wrong, but wouldn't you miss out on the dividend if using options contracts? Let's take TLT for example. Over the last 5 years, it had an annualized return of 5.1%, including dividend. The price has only gone up by 2.2% per year. If we assume you could have bought 50% ITM calls without paying extrinsic value, you would have had 2X leverage against the price action and thus a return of 4.4% per year. That would have been less than just holding TLT unleveraged.

See the last paragraph in the "LEAPS vs Stock Ownership" section of this article:
https://www.nasdaq.com/article/pros-and ... s-cm901256

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Re: On Leverage

Post by pezblanco » Tue Feb 26, 2019 10:11 am

SovereignInvestor wrote:
Tue Feb 26, 2019 8:58 am
Leveraging up and then putting the proceeds in any sort of low risk (especially risk free) bonds is just reckless.  Especially in taxable account where it is horrible for taxes.

The flaw in many analyses here is that yes a blend of stocks and bonds does optimize sharpe...but only of the portfolio using borrowed money.

If we have 100K equity.  And then borrow 50K and are thinking of doing 60/40 stock bond with the borrowed 50K to maximize the sharpe...that is the wrong metric.

The sharpe of the 50K borrowed doesn't matter...Capital is fungible..what matters is the sharpe of the entire portfolio.

So one should keep selling the low risk bonds to deleverage.  Instead of borrowing 50K to have 20K of it in low risk bonds and 30K in equity...just borrow 30K and put it in equity.  Yes the sharpe on the 30K will be lower...but the ENTIRE portfolio of 130K will have better sharpe than if it was 150K and 20K sat in bonds that aren't covering the cost of borrowing.

As far as leverage...using options LEAPS is ideal.  It makes one borrow at the risk free rate since options are collateralized and require margin.

The issue with using ITM Call Leaps to approximate borrowing risk free and buying equities is its not that tax efficient. The best scenario if one profits is they would pay LTCG tax but worse than buying and holding equity underlying if they wanted long term leverage.  Leap calls are essentially being long underlying and long a put so one can do that instead and that is more tax efficient...but theoretically requires borrowing on margin to buy more underlying at rates above risk free....it's more tax efficient though because only the put expires..but if stocks keep rising there's no required tax on the Equity holding. But one must borrow..but if using a put to hedge the risk of margin call is not really there...it's just bad because high cost of borrowing.
I won't pretend to understand very well this last paragraph. I'm interested in learning about this strategy and have to figure a lot of things out. It seems like there are two types of BHs ... those who understand all this and speak to each other in code and those (like me) who need things explained to them like a little child. I have bought (but not received Ayres and Nalebuff's book) ... so I'm trying at least.


Regarding Taxes: I thought that one could just hold the LEAPS call for more than one year and then keep rolling them over. Every time you roll them over you would pay long term capital gains. If the market was down, can you sell them early and tax loss harvest by effectively rolling them over early?

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Re: On Leverage

Post by pezblanco » Tue Feb 26, 2019 10:21 am

EfficientInvestor wrote:
Tue Feb 26, 2019 9:32 am
pezblanco wrote:
Mon Feb 25, 2019 9:49 am
grayfox, the issue really for leverage is always going to be the borrowing rate, right? IB will only give you 1.5% + T-bill for the first 100K (1% + T-bill for sums greater than that), the x leveraged funds have borrowing rates it seems like are something like (x-1)*libor +1, but with their daily rebalancing they suffer quite a bit of volatility drag (maybe another 1.5% to 2% annually?). How about looking at leveraging with options? ... buy long term call options deep in the money (LEAPS). (Yes, I know, this is what Markettimer did in the most famous thread in history on BH ... but it's still a very good idea for getting effective borrow rates quite low. There is even academic research ... see Ayres and Nalebuff) If you're serious about leveraging, this is the next step! :D
Correct me if I'm wrong, but wouldn't you miss out on the dividend if using options contracts? Let's take TLT for example. Over the last 5 years, it had an annualized return of 5.1%, including dividend. The price has only gone up by 2.2% per year. If we assume you could have bought 50% ITM calls without paying extrinsic value, you would have had 2X leverage against the price action and thus a return of 4.4% per year. That would have been less than just holding TLT unleveraged.

See the last paragraph in the "LEAPS vs Stock Ownership" section of this article:
https://www.nasdaq.com/article/pros-and ... s-cm901256
Good point ... dividends (even for the S&P) are an important part of returns aren't they?

alex_686
Posts: 5309
Joined: Mon Feb 09, 2015 2:39 pm

Re: On Leverage

Post by alex_686 » Tue Feb 26, 2019 10:34 am

A couple of points.

I do think that a mortgage can beats out short term lending with leverage, even with the higher rates. It is a non-callable loan. Its long term, so rates are locked so you reduce duration risk. If it is tax deductible, that is a bonus. You would probably need to stretch into corporate bonds instead of treasuries.

Futures probably beat options. There have been some good threads recently about using futures and risk parity. You lever up equity and long bonds, and pay for it with cash and shorting short bonds.

Both futures and options have short term rates built into their price, so no free ride there. Neither will give you access to dividends, but so what? That is also factored in the price. If you are concerned about underperformance due to the missing dividends, just crank up the leverage. In for a penny, in by a pound. The problem with options is that you have to pay for both time and volatility.

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