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Author: imdajunkman Three stars, 500 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 35362  
Subject: A Fibonacci Approach to Portfolio Choice Date: 2/3/2006 8:06 PM
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Leonardo Pisano is better known by his nickname Fibonacci. He was the son of Guilielmo and a member of the Bonacci family (hence, the nickname, right? on the same pattern as “Johnson”). A problem he discusses in the third section of his Liber abaci led to the introduction of the Fibonacci numbers and the Fibonacci sequence for which he is best remembered today:
A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?
The resulting sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, .... This sequence, in which each number is the sum of the two preceding numbers, has proved extremely fruitful and appears in many different areas of mathematics and science.

[Note: the preceding information was cribbed from the source that follows, and the whole article is worth reading.]
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Fibonacci.html

What is noteworthy about a Fib series is that is that it is geometric, rather than arithmetic (such as 1,2,3,4, 5,…). Some people make almost a religion of Fibonacci numbers, ascribing to them the key to the mysteries of the universe. But to me they are just a way of scaling quantities that seem better described by proportional relationships rather than quantitatively equal ones.

Consider the following Fib segment: 3, 5, 8 13, 21, 34, 55, 89. As an investor, what thought immediately leaps to mind? That the series might describe one's annual returns. Let it be so. Think of those numbers as percentages. What might be their frequency of occurrence? How about a reverse Fib series, thusly?

Gains achieved by investors for a one-year period:
3%, 5%, 8%, 13%, 21%, 34%, 55%, 89%.
Percentage of investors who can obtain those gains:
89%, 55%, 34%, 21%, 13%, 8%, 5%, 3%.

The relationship I'm suggesting is that most investors will successfully achieve modest returns, but only few investors will achieve outlierly high ones. Furthermore, lower returns will take less investing effort each week, and they will require fewer skills. So, let's add those two further scales.

Gains achieved by investors for a one-year period:
3%, 5%, 8%, 13%, 21%, 34%, 55%, 89%.
Percentage of investors who can obtain those gains:
89%, 55%, 34%, 21%, 13%, 8%, 5%, 3%.
Time spent per week on investing:
3, 5, 8, 13, 21, 34, 55, 89.
Number of skills needed:
3, 5, 8, 13, 21, 34, 55, 89.

[Note: my apologies for not being able to line up the numbers in columns above each other.

Now comes the interesting part. Ask yourself what type of investing returns you would like to have, and ask yourself what type of returns are possible in the stock (bond) market? In the '90's, it wasn't uncommon for people to tell their financial advisors that they weren't an ambitious or greedy investor and that modest returns like 20%/year would be quite acceptable. [And in hindsight, you're ROTFL, right? both at them and at yourself.]

Nowadays, where on the scale would you put yourself? By his admission, (“I aim low and save high”), Lokicious would locate himself under the 5% return category, or a bit to the right. He wants to have a life, not a portfolio. He has an abundance of the simple skills needed to obtain those kinds of return, not just occasionally when conditions are favorable, and he can obtain them consistently, year after year, in a journeyman like fashion. 5% (or thereabouts) is his bogie in terms of effort expended, skills needed, risks accepted.

(Aside: Loki, if the preceding isn't a fair summary, then I apologize in advance. You make such a clear-cut example that I couldn't bypass you.)

Where might I locate myself? I'd love to flatter myself and say 13%, but across my whole portfolio (not just the junk bond portion), my bogie falls between 8% and 13% in terms of effort expended, skills needed, risks accepted.

I know from private conversation that one of this board's members would be self-ranked under the 21% category or a bit to the left, in terms of effort expended, skills needed, risks accepted.

So the scale, as unlikely as it is, does have utility. Let's see if we can extend its application further.

In a post he made to Spinning, Jack mentioned that his goal was to build a $2.5 million bond portfolio to provide retirement income for his family. Let's guess that the holdings will be investment-grade only and a sustained return of 5% (or a bit to the right of that) is his goal, or a pre-tax income of $125k/year.

(Aside: Jack, I'll make the same advance apology to you as I made to Loki. You are such a clear-cut example that I couldn't bypass you.)

Now, let's work backwards from that $125k figure. If Jack increases his efforts, skills, and risks, higher returns are possible and a smaller portfolio can be obtained (and managed). How much smaller is realistic? Long-time board members have a better sense of Jack than I do, but my impression of his skills is that they are nearly peerless. Throw him into an auditorium with a group of 99 other people who consider themselves investors, give them each a virtual $1 million to invest, and I'd bet that Jack would be the last guy standing. He'd one of the few to consistently achieve positive returns, and, furthermore, those returns wouldn't be modest ones, either.

In short, Jack, I think you are wasting your talents even thinking about messing around with bonds. You've got fundamentalists skills that can take you just about as far to the right on my Fib scale as you want to go. 21%? 34%? 55%? Name your figure. It's there if you want it, but at this price: you'll have a portfolio, not a life, the higher you aim. So let's say that 21% becomes your bogie. That would imply that a portfolio of roughly $595,000 (or one quarter of $2.5 million) would be sufficient to obtain your targeted yearly income (for the obvious reason that your returns would be 4x greater than what you propose).

Sounds great, right? What's the fly in the ointment? RISK. Anyone who is pushing the reward-envelope to the upside is also pushing the risk-envelope to the downside. Yes, gains of 21% or 34%/year are possible and well-documented. But they come at the cost of losses of 21% and 34%/year. (Actually, a bit more due to transaction costs.) Therefore, not the whole of one's portfolio can be invested with “high gearing”. A suitable fraction of the portfolio has to be held as reserves so that the investing program can sustain customary losses and continue forward to achieve, on average, its targeted returns. In other words, drawdowns will happen, and cash has to be there to cover them. (This was the nature of the failure of LTCM. The academic advisors had committed all capital. There were no reserves and no way to unwind risk.)

So, let's set up the Fib series again, using the first row to indicate targeted returns, the second row to indicate standard deviation of returns, and the third to suggest prudent reserves.

Gains: 3, 5, 8, 13, 21, 34, 55, 89.
StDev: 3, 5, 8, 13, 21, 34, 55, 89.
Reverves: 3, 5, 8, 13, 21, 34, 89.

In other words, portfolio planning is likely a matter of ”You take the high road, and I'll take the low road, but we both will likely get there at the same time and both need to carry the same equivalent burdens.” And why might that be so? Because risk is risk, wherever it is found, and reward will always be proportional to risk.

So, if a person wants an annual portfolio income of $50,000, then she can have a $1 million portfolio and stick to a safe and easily managed vehicle like Treasury bonds. A quick review once a week and some minor paperwork is all she needs to do to stay on task and on target. The rest of her time and life become her own. Or she can put in an 89 hour week, aggressively managing a much smaller amount of money and achieve the same $50k annual goal (provided she is carrying sufficient reserves, and how much smaller is a detail that would need to be worked out). So, let's run through an example.

The Fib series predicts that a targeted return of 21%/year would require a 21% reserve. Let's assume that a 5% return could be expected on reserves. The invested 79% of the portfolio will gain 21%. Therefore, the effective return becomes 17.6%. To obtain an annual income of $125k, assets under management would have to roughly $710K, which is a lot more obtainable goal than $2.5 million and has this further advantage. Gains from a portfolio of investment-grade corporate bonds is going to be taxed at ordinary income rates. Gains from a portfolio that is achieving annual returns of 17.6% is going to include gains that are taxed at the lower, cap gains rate. What matters to a family isn't their pre-tax income, but their after-tax income. $125k taxed at 30% is no better than $109k taxed at 20%. Moving to the right of the scale (where gains are less dependent on ordinary income) means that less money has to be managed.

Caveat: In real-life investing, calculating the reserves necessary for each portfolio would have to be done with real data, not the fiction-free modeling I'm indulging in. The procedures for doing such back-testing are well known to traders. Regrettably, investors are mostly unaware of the process.

Thus, the consequence of a Fib-oriented, portfolio-choice scale seems to be this. Ends and means both have to be considered in constructing and managing a portfolio, and a very important factor is the investor herself. She (or he) might want returns of 21% per year (or might need them due to a late start toward building a retirement fund). But unless she is willing to put in the weekly management hours and acquire the needed skills and has sufficient capital to create the reserves to handle the risks, her goal of 21% is unrealistic. She might have a lucky year or two, but the smart bet has to be that she will blow up her account, if not in this market cycle, then the next one. She lacks sustainability.

But, if she is willing to do the work, has the skills and capital, then the path she choose is no more risky than the path of the Treasury-bond buyer. The paths are simply different. Both persons will achieve their goals with an equivalent degree of assuredness. That's not a theorem I can prove. But it is an insight that I trust. Who each person is as-a-person is who they can be (or want to be) as investor. Some people are most comfortable to the far left of the scale; some, to the far right; some, in the middle. Where the mistakes happen is in the mismatches that investors make between themselves and the time-effort-skill-risk-reward scale. I've proposed a “portfolio choice” scale. Feel free to borrow it, but I'd suggest, for the exercise to be useful, that you really need to build your own.

Charlie
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Author: Lokicious Big gold star, 5000 posts Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 15211 of 35362
Subject: Re: A Fibonacci Approach to Portfolio Choice Date: 2/3/2006 10:45 PM
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"By his admission, (“I aim low and save high”), Lokicious would locate himself under the 5% return category, or a bit to the right."

Close. If my projections, with not that many years to go, for savings, modest returns, and inflation, prove close, I believe we will begin retirement, c. 64/63, with an initial withdrawal rate of less than 3% (around 2.5% if the bond traders are right about inflation). This is sustainable for 40 years with a return of 2% (actually somewhat less) above inflation, and I'm ignoring social security and property.

2% above inflation on high grade bonds/CDs has usually been achievable, which is why I'm not happy with current low yields. I hope the % in stock index fund can get 3% above inflation over the long haul, so 2% in all shouldn't be too hard. The problem is I am increasingly pessimistic about the US economy, but rationally getting more aggressive when this kind of modest return has always been easy to come by, makes no sense.

On the up-side, between global warning, other environmental disaster, the likelihood of epidemic from drug resistant bacteria or some virus, a violent free-for-all battle over dwindling resources or between Armageddon factions of different religions, total international economic collapse, complete entrenchment of the oligarchy, and so on, makes it unlikely outliving our savings will be the most important issue we will face.

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Author: jrr7 Big gold star, 5000 posts Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 15213 of 35362
Subject: Re: A Fibonacci Approach to Portfolio Choice Date: 2/4/2006 12:08 AM
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The relationship I'm suggesting is that most investors will successfully achieve modest returns, but only few investors will achieve outlierly high ones.

What about people who achieve spectacularly low returns, like -99%?

I'm not kidding.

The "expected distribution of returns" is one of the key areas of study in economics.

Obviously you can't lose more than 100%, and your potential gain is unlimited.

I assume most people have heard of the "normal distribution" also known as the bell curve. It predicts things well for linear processes (e.g. sum of several die rolls) but not as well for geometric processes.

One distribution that fits geometric processes well is the Lognormal distribution (the logarithm of the return is normally distributed). Looks something like:

|
| ...
| .. ..
| . ..
| . ...
| . ...
| . ....
| .
| .
|.
+-----------------------

A very few people lose it all, most people perform in the average range, and a very few people do spectacularly well.

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Author: imdajunkman Three stars, 500 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 15214 of 35362
Subject: Re: A Fibonacci Approach to Portfolio Choice Date: 2/4/2006 9:41 AM
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Loki,

How do you estimate inflation for the purposes of managing your porfolio?

I can't believe you accept the government's lies (as summarized in the CPI). Therefore, you must be creating your own benchmarks. Would you share them?

Charlie



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Author: WendyBG Big gold star, 5000 posts Top Favorite Fools Top Recommended Fools Feste Award Winner! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 15220 of 35362
Subject: Re: A Fibonacci Approach to Portfolio Choice Date: 2/4/2006 2:58 PM
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<Obviously you can't lose more than 100%>

By using leverage, and investing in options, you can lose more than 100%.

Wendy

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Author: Wradical Big gold star, 5000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 15221 of 35362
Subject: Re: A Fibonacci Approach to Portfolio Choice Date: 2/4/2006 3:38 PM
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By using leverage, and investing in options, you can lose more than 100%.

Wendy

____________________________________
Or by selling short.

Bill

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Author: DrTarr Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 15222 of 35362
Subject: Re: A Fibonacci Approach to Portfolio Choice Date: 2/4/2006 3:56 PM
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Lets split the options in to two categories!!

By using long options, you limit yourself to 100% of the option, which can reduce your risk!

A wonderful tool for risk aversion.

DrTarr

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Author: jrr7 Big gold star, 5000 posts Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 15234 of 35362
Subject: Re: A Fibonacci Approach to Portfolio Choice Date: 2/5/2006 5:49 PM
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By using leverage, and investing in options, you can lose more than 100%.

Even something as simple as shorting a stock has an unlimited loss potential. But if your broker has any sense at all, he will have made a margin call requiring you to either post some collateral as security, or liquidate your position, long before you reach losing everything.

If you post more securities, you have increased your investment and thus haven't lost more than 100%.

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Author: jrr7 Big gold star, 5000 posts Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 15278 of 35362
Subject: Re: A Fibonacci Approach to Portfolio Choice Date: 2/7/2006 10:10 PM
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By using leverage, and investing in options, you can lose more than 100%.

I don't know what I was thinking when I challenged this. Yes, that is correct, and the lognormal return graph only applies when you OWN an asset, not when you are borrowing or shorting.

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