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Leverage versus Asset Allocation: Which Gets Better Returns with Lower Volatility?
Old 03-30-2008, 08:33 AM   #1
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Leverage versus Asset Allocation: Which Gets Better Returns with Lower Volatility?

Was looking to see if there had been an in-depth discussion of whether changing asset allocation versus adding modest leverage is a better way of increasing investment returns. Which approach gives better returns with less volatility?

If you create the right amount of asset allocation, you get to the spot on the efficient frontier curve of highest return and least volatility. I have an asset allocation approach that considers equities, inflation sensitive assets, deflation sensitive assets and relative value as separate asset types. I'll hold the debate of what the right mix is for now.

Now if once the investor finds the spot on the efficient frontier curve that has the best return for volatility -- should an investor change their asset allocation to improve returns or is it better to add modest leverage? If believe that if interest rates are modest such as today, e.g., current after-tax interest on mortgages are in the 3-4% range, it makes sense to add leverage to a low volatility portfolio rather than shift the asset allocations towards more equity.

However, I've noticed that the "conventional wisdom" that most people follow using traditional investment advice would have them shift their asset allocations to higher equity allocations if they want higher returns.

I would rather have lower volatility and higher returns. Going up the black line in the second graph offers higher returns with less volatility than having a pure equity portfolio.This offers a better solution in my opinion.
I've put the efficient frontier graphs and potential additional return form leverage on my blog as I couldn't figure out how to paste them on this post.

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Now we can debate what the optimal amount of leverage is. Lots of people get worried about leverage or mindlessly seek leverage. As a Dave Ramsey fan, I can appreciate the "debt free" mindset. However, I also like to get better returns.

So my current approach to adjusting leverage is as follows.

1. My top leverage at this point that I will allow myself is 30% on total assets, but in general my rules are to keep this below 20% in general as I can't handle the higher volatility.

2 I tend to look at equity valuations and look at the valuations of the markets based on smarter people than I , such as GMO.

3. When the market is overvalued (e.g., low 10 year returns are expected) -- that's the good time to cut leverage -- maybe all the way to zero, or even raise some cash.

4. When the market takes a drop and valuations start to look better -- that's the time to increase leverage.

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Old 03-30-2008, 09:11 AM   #2
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when you find the point to start using leverage let us all know as we lack that ability. asset allocation works best when your wrong
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Old 03-30-2008, 09:36 AM   #3
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According to your blog, you earn $1MM/year in after-tax income and have a net worth of $2.6MM. Why even bother messing around with leverage? If I had that kind of cash flow, I'd do 50/50 stocks/bonds and move on to enjoying life rather than trying to find the perfect spot on the risk/return bullet.
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Old 03-30-2008, 09:50 AM   #4
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Yes leverage can be effectively employed.

But using margin accounts introduces other risks. Unless one is both a knowledgeable disciplined investor (with a good plan) that keeps a fairly close eye on things... going long in a well diversified portfolio of stocks and bonds is a more safe bet over the long-haul.

I do not believe employing leverage is the best move for most people.
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Old 03-30-2008, 11:06 AM   #5
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I agree that leverage is too risky for most people. I have never bought securities on margin and current market conditions make that decision seem like a good one.

However, now that I am FI (NW is approximately that of the OP), I have recently introduced some investment real estate (a new asset class for me) using leverage. I put down <$40K on a suite in a professionally managed building. My tenants are paying the mortgage and expenses. Over time my equity will increase and when the mortgage is paid, the rental income will supplement my retirement. I consider this a fairly low risk investment since it is in an upcoming and undervalued area and is well managed and being upgraded. Since I will not have a pension I see future rental income adding stability to my retirement funds, almost like an annuity. I may add to my real esate portfolio, but I will never leverage >10% of my NW. Thanks to Martha's cautionary advice I have also decided to stay away from limited partnerhships, which the OP's profile indicates he has been burnt on.

So I think it's a matter of choosing whether you are comfortable with leverage, and selecting carefully according to the inherent value of the investment and your own risk tolerance.
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Old 03-30-2008, 01:38 PM   #6
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Your efficient frontier of risky assets is somewhat peculiar in that increasing risk by increasing the allocation to equities appears to reduce the expected return. That is not the usual case with the efficient frontiers I have seen. In fact, the only way to increase expected return by increasing risk with your efficient frontier is to use leverage.

However, even with a more traditional-looking efficient frontier, if your tangent line, which combines the optimum portfolio of risky assets, with the borrowing cost, produces a higher expected return for the same level of risk, it is obviously optimal. That is to say, the tangent line becomes the efficient frontier. This is a standard portfolio theory result.

Thus, the question is reduced to how much risk you want to take. Once you have determined that level, you should use leverage (if it's to the right of your optimum portfolio) since, from your diagrams, that will always lead to a higher expected return for the same level of risk.
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Old 03-31-2008, 12:01 AM   #7
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What is the cost of leverage?

How do you define leverage?

Technically, anyone holding a mortgage / student loan debt is effectively leveraging if they are investing for retirement before paying off those items.
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Old 03-31-2008, 10:50 AM   #8
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Thanks for the questions

I've changed the efficient frontier graph to reflect a more traditional curve.

I don't know what the market is going to do ; however, I think it is reasonable to look at the market from a valuation flow, which some services do -- see www.GMO.com for a monthly assessment of 10 year returns.

I do define leverage as anything being above being completely debt-free. So I approach the question if everything is fully paid off, do I still want to borrow money. At this point the answer is yes, but only up to 20% of total assets.
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Old 03-31-2008, 11:29 AM   #9
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Gryffindor, your cost of the leverage funds is greater than what you can get in an all fixed-income portfolio, correct? If so, then all of the leverage money should be invested in equities (it wouldn't make sense to borrow at say, 8%, then invest that cash @ 6%). Then the leveraged portfolio will push the portfolio point further toward the 100% equities point, and your tangent line will have a lower slope than what is shown in your graph. So, in effect, you're not at the efficient portfolio point anymore.
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Old 03-31-2008, 12:12 PM   #10
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Quote:
Originally Posted by Patrick View Post
Gryffindor, your cost of the leverage funds is greater than what you can get in an all fixed-income portfolio, correct? If so, then all of the leverage money should be invested in equities (it wouldn't make sense to borrow at say, 8%, then invest that cash @ 6%). Then the leveraged portfolio will push the portfolio point further toward the 100% equities point, and your tangent line will have a lower slope than what is shown in your graph. So, in effect, you're not at the efficient portfolio point anymore.
I don't think this is correct. The relevant thing is that the optimal portfolio has a higher return than the borrowing cost. The fact that part of your borrowing (at 8%) is invested in fixed-income (at 6%) doesn't matter. You are leveraging the combination of assets, which cannot be obtained without including some fixed-income. Another way to think about it is that you are accepting some negative return on the fixed-income piece in exchange for the lower correlation coefficient, which improves the overall risk-return characteristics of the combination.
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Old 03-31-2008, 03:06 PM   #11
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Originally Posted by FIRE'd@51 View Post
I don't think this is correct. The relevant thing is that the optimal portfolio has a higher return than the borrowing cost. The fact that part of your borrowing (at 8%) is invested in fixed-income (at 6%) doesn't matter. You are leveraging the combination of assets, which cannot be obtained without including some fixed-income. Another way to think about it is that you are accepting some negative return on the fixed-income piece in exchange for the lower correlation coefficient, which improves the overall risk-return characteristics of the combination.
This makes zero sense to me. You're going to deliberately take a 2% loss on the fixed-income part of the leverage? How can that possibly improve your overall return? :confused: That would have to be made up somewhere else, presumably from the equity portion, so I'm pretty sure you'd be better off just leaving that part out.
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Old 03-31-2008, 04:13 PM   #12
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Here's the math on a sample efficient portfolio with a return of 10% and a cost of leverage of 5.5%:


Return 10%
Cost of Leverage 5.5%

Leverage Return
0% 10.00%
10% 10.45%
20% 10.90%
30% 11.35%
40% 11.80%
50% 12.25%

So an extra 30% leverage gets you an extra 1.35% absolute return with lower volatility if your asset allocation is right. The real question is if this has a lower volatility than a much higher equity portfolio. If you use historical betas for the market, I believe it does (don't have those in a spreadsheet right now).

Patrick, if you create the portfolio you are advocating you're ultimately increasing the volatility of the portfolio by having a higher percentage of equity. That may be your objective but it doesn't necessarily increase volatility by as much as is possible.
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Old 03-31-2008, 04:22 PM   #13
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Originally Posted by gryffindor View Post
Patrick, if you create the portfolio you are advocating you're ultimately increasing the volatility of the portfolio by having a higher percentage of equity. That may be your objective but it doesn't necessarily increase volatility by as much as is possible.
So are you saying that you would borrow money and put part of into fixed income also? If so, please explain how you're making up the difference in interest rates.
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Old 03-31-2008, 04:33 PM   #14
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Originally Posted by FIRE'd@51 View Post
I don't think this is correct. The relevant thing is that the optimal portfolio has a higher return than the borrowing cost. The fact that part of your borrowing (at 8%) is invested in fixed-income (at 6%) doesn't matter. You are leveraging the combination of assets, which cannot be obtained without including some fixed-income. Another way to think about it is that you are accepting some negative return on the fixed-income piece in exchange for the lower correlation coefficient, which improves the overall risk-return characteristics of the combination.
An investment that returns less than it costs will be a drag on any portfolio, no matter how much of it you leverage. Look at people paying 5% mortgages while holding 4% bonds. Tax-deductible, tax-deferred, blah blah, put all the assets into terms of after-tax dollars and the result is that paying higher rates to hold lower returns will not work any better in our ER portfolios than it worked for Long-Term Capital Management.

The cash part of a portfolio would be necessary for living expenses in a down market. And that's because leverage works great... right up until the margin calls start coming in.

The whole concept smacks of "We lose a little on each transaction, but we really make it up on volume!!"
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Old 03-31-2008, 05:13 PM   #15
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An investment that returns less than it costs will be a drag on any portfolio, no matter how much of it you leverage.
I agree, but that's not the case here. If you look at the graph of the efficient frontier with borrowing costs that the OP has presented, you can see that the optimal portfolio has a return greater than the borrowing cost, so there is no drag - rather it's an enhancement.
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Old 03-31-2008, 05:48 PM   #16
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Originally Posted by FIRE'd@51 View Post
I agree, but that's not the case here. If you look at the graph of the efficient frontier with borrowing costs that the OP has presented, you can see that the optimal portfolio has a return greater than the borrowing cost, so there is no drag - rather it's an enhancement.
You mean the graph with no numbers on the axes or the graph with the other-than-historical data?

I could be reading the numbers wrong, but here's what I think I see from his example:
Quote:
Originally Posted by gryffindor View Post
Here's the math on a sample efficient portfolio with a return of 10% and a cost of leverage of 5.5%:
Return 10%
Cost of Leverage 5.5%
Leverage Return
0% 10.00%
10% 10.45%
20% 10.90%
30% 11.35%
40% 11.80%
50% 12.25%
Let's assume that a $100K unleveraged portfolio returned $10K at the end of the year.

Let's borrow another 50% ($50K) at 5.5%. That'll cost us $2750 over the first year (minus some tax deductions and other details). We achieve a return of 12.25%, or $12,250. When we pay back the $2750, that leaves us with a return of $9500.

Perhaps we need to try this with better numbers. I'm open to suggestions.
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Old 03-31-2008, 07:37 PM   #17
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Quote:
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You mean the graph with no numbers on the axes or the graph with the other-than-historical data?
The one with no numbers - Expected Return vs Expected Risk with a positively sloped tangent line from the Borrowing Cost intercept to the Efficient Portfolio. To the right of the Efficient Portfolio the tangent line becomes the efficient frontier, so a levered Efficient Portfolio dominates.

The effect you are describing (where there is drag) would occur if the borrowing cost were raised to the point that no tangent line could be found. The line originating at that borrowing cost would slope downward and intersect and pass through and under the efficient frontier.
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Old 03-31-2008, 08:39 PM   #18
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I think the model is seriously flawed if it leads you to believe that you can make more money by giving money away (unless you believe in Karma also).
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Old 04-01-2008, 09:27 AM   #19
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To answer Nords and Patrick's questions:

My table was the net result of both the cost of capital and the return of investment. The assumptions of the return of 10% was for the efficient portfolio and the cost of capital was 5.5%.

So to use Nord's example of borrowing 50% on 100k (way too much leverage by the way). The return of 150k would be 15k. The cost of 5.5% interest on 50k would be 2.75k. So the total return would be 12.25k or 12.25% (what the table says).

Many people have commented in the thread that additional leverage is risky. I agree. I think only a modest amount (max 30%) is acceptable.

However, I think 100% equity portfolio is risky too. The key question is to ask is moving from a diversified portfolio to a higher percent of equities in order to get higher return more risk or less risky than leverage.

The way I use leverage is through a mortgage -- so no margin calls ever.

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Old 04-01-2008, 11:19 AM   #20
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I don't think anyone should have 100% equity portfolio, regardless of age.

There is no material difference between a 90/10 vs. 100% equity portfolio over longer timeframes as measured by returns. One does enjoy reduced volatility by doing so however.
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