Portfolio Selection

Discussions about the testing and simulation of mechanical trading systems using historical data and other methods. Trading Blox Customers should post Trading Blox specific questions in the Customer Support forum.
drm7
Roundtable Fellow
Roundtable Fellow
Posts: 96
Joined: Sun Apr 20, 2003 9:02 pm
Location: Richmond, VA

Portfolio Selection - Small (<50k) Trader

Post by drm7 »

I apologize in advance if this question/comment seems a little "tactical."

I have some possible alternatives for people (like me :wink: ) with small accounts. I do agree that it is difficult to deal with the large amount of risk that an average futures contract exposes a small trader to - a T-note contract can swing $1,000 in a single day (5% of a $20k account). Currency futures are similar. Some meats and grains are better, but there are very few markets which have acceptably low contract sizes/volatility.

My recommended solution is one or a combination of three alternatives.

1) Low volatility commodities:

-Corn/Oats
-Soybeans (maybe)
-Eurodollar
-Sugar
-Cocoa (although not lately!)

I'd like people's feedback on mini-contracts - The small size makes the flat commission rate/contract a pretty high % of ATR!

2) Currencies on OANDA (no minimums - position sizing to the exact dollar)

Pick 3 crosses which touch all six of the following - but don't repeat:

-USD
-GBP
-EUR
-JPY
-CHF
-AUD or CAD or ZAR

Three crosses can be set up to have almost zero correlation. Since everything is relative, an economic shock won't take all of them down (read Fooled by Randomness for a new appreciation of economic shocks!)

3) A stock ETF, such as SPY or QQQ (not both)

I think that stocks are far more correlated than people think - that's why there were so many "geniuses" in the last bull market - EVERTHING was going up (and then came crashing down)! If the market trends nicely, trade the whole market.

//End Strategy//

My rationale? Correlation, correlation, correlation. I have done simple betsizing simulations in excel, and I have come to two conclusions:

1) Max drawdown is a direct function of %losing trades + % bet per trade.
2) Rate of return is expectancy + # of trades per annum + % bet per trade.

Therefore, a profitable system needs more positive trades, and a "safe" system needs short losing streaks, with minimized betsize per loss.

In order to get a lot of trades, a futures trader needs to be in a lot of markets so they can catch a lot of trends. Unfortunately, being in too few markets will lead to a probability of no trends. More importantly, they need to be in multiple non-correlated markets so they aren't simply doubling and tripling their betsize.

If one trades two correlated markets (e.g. T-Bonds and T-Bills) that person is simply doubling their bet.

The method described above seems to scratch together enough low-correlation markets (with acceptable risk parameters) to make a go of it.

OK, time to stop blabbering :oops:

I have a few "issues" with this strategy

1) Brokers - I would have to spread my meager capital among multiple brokers (Interactive Brokers comes the closest to an integrated platform, but doesn't offer spot currencies or softs/grains)

2) Spot FX margin - Contrary to popular belief, most spot FX dealers let you use less leverage than the futures exchanges. OANDA at most gets you 30:1, but a yen contract on the IMM can be had at 50:1. I am "trading" on their FXGame platform, and see that, with a 2N stop, 1 unit takes 5% of my equity. That means that only 3 "loaded" pairs will use up 60% of my equity on margin (3*4*5%) Not a lot left over for much else!

3) Commodity choices - Is there something missing about small account sizes? Does the system degrade because 1.68 contracts rounds down to 1 or simply because there aren't enough markets to find trades?

Two alternatives

1) Go "whole hog" with Spot FX, knowing currencies are very trendy, and I can get low correlation. Are three non-correlated pairs enough?

2) Find an acceptable mix of commodities/mini contracts, and perhaps single stock futures (liquidity problems?) without FX and accept less control over exact position-sizing.


Please comment on my portfolio/issues/alternatives.

OK, this time I really am going to stop blabbering!
Sir G
Moderator
Moderator
Posts: 243
Joined: Wed Apr 16, 2003 12:21 am
Location: Salt Lake City, Utah

Amoebae Allocation

Post by Sir G »

At this point, I find myself not trying to engage in answering questions but in offering more food for thought. My hope is that answers will be found as this food is digested.

Another way to look at the opportunity of Portfolio Selection would be another story that could have run parallel with "The Brothers, Goldie Hawn" it could have been entitled, "The Partners, Jimmy George."

While I'm going to spare everyone from another story, it could be read in Market Wizards (Page 305-306). Jimmy & George are Jimmy Rogers & George Soros.

The gist of it is:
When you were trading leveraged products such as commodities and currencies, how did you determine what your allocation was?

Jimmy Rodgers: "Until we ran out of money, we were always leveraged to the hilt. When we bought something and ran out of money, we would look at the portfolio and push out whatever appeared to be the least attractive item at that point. For example, if you wanted to buy corn and ran out of money, you either had to stop buying corn or sell something else. It was an amoebic process. You know how amoebas grow – they grow out this way, then they run into pressure so they grow out the other way. It was a very amoebic portfolio.

While there is more then one way to skin a cat (forgive me PETA) could there be other (dare I say better) creative ways to allocate positions to your system? For both large & small accounts?

Have you ever noticed if you hold onto something as precious & dear, that you will find in most cases that will be as good as it gets for you as it becomes your glass ceiling? Contrast that to you letting go of what is held precious & dear and you find that in most cases, something else much better replaces what you have released?

Giving freedom to what you hold so dear, allows growth and opportunity.

Just some thoughts.

Sir G
Robert Nio
Senior Member
Senior Member
Posts: 41
Joined: Thu Apr 17, 2003 11:34 am
Location: Palo Alto, California

Post by Robert Nio »

Sir G.,

well said ... this is true in many areas ... e.g. kids :-)


Never EXPECT ... but DO react !

Robert
Bondtrader
Roundtable Knight
Roundtable Knight
Posts: 101
Joined: Mon Apr 28, 2003 11:07 am
Location: Zimbabwe

Post by Bondtrader »

The conventional-wisdom recommendation "Dont trade correlated markets" is often repeated but seldom tested. I decided to run a couple of tests myself ....
Fascinating :shock: stuff. Quite a bunch of numerical results too, at this URL:

http://traderclub.com/discus/messages/1 ... #POST13210
Kiwi
Roundtable Knight
Roundtable Knight
Posts: 513
Joined: Wed Apr 16, 2003 1:18 am
Location: Nowhere near

Post by Kiwi »

That is a great bit of research on Mark's part.

It seems to me that it suggests that the issue is not

Statistical correlation between markets but
Statistical correlation between closed trade equities
. . . (Turtle measure vs OTE) or
Statistical correlation between open trade equities
. . . (Commonly used to determine equity for next bet size)

Thus we should build our portfolios by mixing combinations of systems with markets and choosing those pairs that, amongst other measures, have low correlations.

Any opinions on this?

John
Karakoram
Roundtable Knight
Roundtable Knight
Posts: 127
Joined: Wed Apr 16, 2003 11:01 pm
Location: Reno, NV
Contact:

Post by Karakoram »

you said: "that, amongst other measures, have low correlations. "

You are assuming that low correlations will continue into the future, or said another way, you are assuming that the past will be repeated in the future.

My belief is that this is a mistake to assume that the past will repeat in the future.

You could, just as easily, say that "I will pick markets that are highly correlated in recent history, with the assumption that the markets will become less correlated."

or, you could say "I will assume that I can never know which markets will be correlated in the future, so I will just trade as many as my capital allows."
forex_kid
Senior Member
Senior Member
Posts: 47
Joined: Thu Apr 17, 2003 5:30 pm
Location: Sacramento, CA

Three pairs enough?

Post by forex_kid »

drm7 - On the "Whole Hog forex" question....


three pairs... hmm.

I've put a *lot of time into hand cleaning ten years of spot FX daily price data from FXCM and then running correlation matrices in excel, and the simple answer seems to me that I would feel "comfortable" with more than 3 pairs. I'm using < abs60% correlation as my current "comfort" level between loosely and strongly correlated, but picking that # is a whole 'nother issue.

Here's the four majors:

gbpUSD eurUSD usdJPY usdCHF
gbpUSD 100.00%
eurUSD 95.70% 100.00%
usdJPY -23.61% -16.79% 100.00%
usdCHF -93.72% -96.96% 3.31% 100.00%


I'm currently working on a dynamic 3d visualization of the correlation amongst the 17pairs that looks a bit like a painted desert, with lots of peaks, valleys and plateaus.

My goal is to be able to plug currently active trades into the front end (for example, three live trades in three different pairs) and then input a proposed new trade, and see how it is correlated against each of the individual already active positions as well as how strongly it is correlated with the active positions as a whole.

Of course, karakoram hits it out of the park with his questions about the relative value of any of this... :idea:


-Morgan
Robert Nio
Senior Member
Senior Member
Posts: 41
Joined: Thu Apr 17, 2003 11:34 am
Location: Palo Alto, California

Post by Robert Nio »

Just my $0.02:

I hear many good ideas about diversification and portfolio management but I see a lot of focus / efforts on something, which is important, but has only a minor effect on your equity line at the end of the day.

IMO, applying just plain common sense to your securities selection, avoiding the obvious correlations, will give you 90% of what you can get in terms of diversification and the effects on your equity line.

I am curious to see that there is truly a significant difference between this simple approach and when you try to construct your portfolio as orthogonal as possible.

Happy Trading

Robert
Karakoram
Roundtable Knight
Roundtable Knight
Posts: 127
Joined: Wed Apr 16, 2003 11:01 pm
Location: Reno, NV
Contact:

Post by Karakoram »

YES! Thank you Robert. YOu said it better than I was trying to say it.
forex_kid
Senior Member
Senior Member
Posts: 47
Joined: Thu Apr 17, 2003 5:30 pm
Location: Sacramento, CA

boredom...

Post by forex_kid »

Yes indeed Robert,

That's the question I'm struggling with getting clear about.

Is there real value to putting lots of time into correlation, or is it just my current way to keep stimulated when the actual work of trading is almost actuarial in feel?

I'd love to hear any perspectives or research on the relative value of heavy optimization of corellation.


Cheers,

Morgan
Sir G
Moderator
Moderator
Posts: 243
Joined: Wed Apr 16, 2003 12:21 am
Location: Salt Lake City, Utah

Post by Sir G »

A few of the things that I have never understood about correlation as applied to portfolio selection are:
  • On any given day the markets can only go up, go down or stay flat.
  • A trading system needs to go long, go short or stay flat.
  • Money is made when your longs go up and your shorts do down.
  • Hence, we need to encourage our longs to go up and our shorts go to down.
Beyond “interesting” reading, I have never understood how something that is in such a state of flux and limiting in its nature has some sort of ability to direct or enhance our opportunity which is limited to just going long and going short.

I don’t know about you, but I have always wanted ALL my longs to go up and ALL my shorts to go down (that is why we buy & sell) and in that regard, we enter into longs wanting/expecting them to go up and wanting/expecting our shorts to go down. When we have to work within such a limiting world of up or down, doesn’t correlation need to be a good thing? And isn’t measuring it in the spirit of portfolio selection also a mute point?

Sir G
forex_kid
Senior Member
Senior Member
Posts: 47
Joined: Thu Apr 17, 2003 5:30 pm
Location: Sacramento, CA

pencils and erasers

Post by forex_kid »

Sir G,

The arguement I've always heard is that if you:

A) Test your system with 2% risk per market 6% portfolio

B) Trade three markets, pencils, erasers, and scissors

C) Get three new buy signals and open a 2% position in each



****If pencils and erasers tend to historically move together (i.e. if you mixed up the labels for the data, you couldn't tell) then if your long signals for pencils and paper happen to get stopped out, you've lost four percent on essentially one trade/signal.


What are your thoughts?

-Cheers,

Morgan
Kiwi
Roundtable Knight
Roundtable Knight
Posts: 513
Joined: Wed Apr 16, 2003 1:18 am
Location: Nowhere near

Post by Kiwi »

Karakoram,

I agree with your 4/29 3:05 supposition that market/system pairs that havent been correlated in the past will probably/possibly correlate in future. See my earlier posting above 4/19 11:47:
Despite this I think it pays to over diversify to allow for the possibility that historically uncorrelated market/system combinations may correlate in future. I think that it also pays to trade a proportion of your equity with different timeframes because in a period where long trends dont occur, short sharp ones may occur.
I dont agree with your second suggestion/option:
"I will assume that I can never know which markets will be correlated in the future, so I will just trade as many as my capital allows."
I would suggest that you can look at market/system correlations in the same way that you avoid overoptimisation of parameters. To determine my own pairs what I did was divide the historical period into 5 overlapping time zones. I then looked at MARs in each period to try to find evidence that the pairs might slip in and out of correlation. My goal in doing so was to avoid optimising my choice of uncorrelated pairs.

Although I did not do so, you could test your two options by looking at the historical data and finding out whether a mix of uncorrelated pairs in 5 year period a) was more or less likely to be correlated than a random or common sense choice in periods b), c), d) and e).

I think that a similar approach should give you a somewhat better result than straight common sense (you could have done better with better tools as my tools were tradestation and massive excel spreadsheets or if you had more knowledge of the statistical tools for making these comparisons). My reason for suspecting this is this is that some of the options I rejected after testing were ones I would have included with my version of common sense.

It did fail during the prewar shock but it may still have been better than some combinations of Robert's "just plain common sense". I guess it would depend on how good the person applying common sense was and how lucky (starting to sound a little like system vs discretionary trading argument).

Conclusion: I think it is worth seeking a market/system mix using the same approaches (multiple time period samples) you would use to minimize system development optimization but I havent developed a proof. It doesnt have to take long (a couple of weeks once off to develop and populate your test harness and then a few hours when considering a new system/market pair). I also think that you should overdiversify to allow for future periods where probabilities conspire to produce correlation.

At the very least you are likely to avoid the worst common sense errors.
Kiwi
Roundtable Knight
Roundtable Knight
Posts: 513
Joined: Wed Apr 16, 2003 1:18 am
Location: Nowhere near

Post by Kiwi »

Sir G,

My understanding of the value of seeking uncorrelated market/system pairs is that it relates to the times of loss not the times of gain.

I agree that all going up at the same time is a great thing.

The problem as I perceive it is that if you trade, say, aberration on one commodity, say, corn and you look at it for 20 years you find that you make $17,987 on one contract. In that same period your max DD is $2,687. If you say a 50% drawdown is the max acceptable then you need (yes I know that this is no compounding and not taking into account when the DD occurred - lots of approximations) $5374 of capital giving a return of 16% per annum (17,987/5374/20*100).

For me this is not enough. So what you do is take 5 commodities (say) that have similar characteristics BUTTTT the maximum drawdowns occur at different times.

So (if they are perfectly uncorrelated) you make 5x17987 and each commodity has its 2687 drawdown at a different time. So once again I need 5374 to trade the system but I now get $89935 over 20 years which is a return of 84% per annum .... Yeee haaa, now we are cooking!

So correlation is about getting market/system pairs that are unlikely to have their drawdowns at the same time. This lets you bet muchhh heavier which gives you a higher return. The risk that you take is that the market pairs will correlate in future and you will be ruined :cry:

Does this make sense? I would be interested in your views on the value of seeking uncorrelated market/system pairs (or any other approach he considers to have merit).

John
Bondtrader
Roundtable Knight
Roundtable Knight
Posts: 101
Joined: Mon Apr 28, 2003 11:07 am
Location: Zimbabwe

Post by Bondtrader »

People are theorizing: what results would I get, if I ran this test?
The answer is, of course: run the test and find out. No theorizing necessary.

People are also asking: what if something really bad happens in the future, that never happened in the past? What if I'm long Swiss Franc and short Coffee, and on the same day they devalue the SF by 100-to-1 AND the entire coffee crop in both Brazil and Vietnam suddenly dies in 5 minutes with no warning? It never happened in the past, it never happened in backtesting? The answer is, of course: this is a price shock and you are screwed. Prudent traders use stop-loss orders in an attempt to lessen the devastation; more conservative traders employ heat limits and sometimes group-heat limits; paranoid traders like Nassim Taleb only trade option strategies which strictly limit their risk to known amounts even during wild price shocks. All of them are going to lose money during a price shock, especially a shock that gaps well beyond stoploss prices, very especially a shock that goes limit-locked several days in a row.
Forum Mgmnt
Roundtable Knight
Roundtable Knight
Posts: 1842
Joined: Tue Apr 15, 2003 11:02 am
Contact:

Post by Forum Mgmnt »

Hmmm, a very interesting discussion so far.
bondtrader wrote:The answer is, of course: run the test and find out. No theorizing necessary.
Music to my empiricist ears... But first, back to the theory...

From my point of view, diversification serves to smooth the equity curve and improve risk-adjusted returns in two significant ways:

1) Two instruments that have positive equity curves and less than 1.0 correlation will nearly always have a smoother overall combined equity curve. As John/Kiwi points out, this is because the peaks and valleys don't match up. The added smoothness diversification provides allows you to bet larger than you would otherwise be able to bet for a given amount of risk.

This is both good and bad. It can be good because smooth is better than jagged. It can be bad because a weaker instrument can dilute the upside power of a stronger instrument. Thus there is a tension in diversification between power and smoothness.

2) Two instruments that aren't perfectly correlated offer higher betting frequency (i.e. more trades) when compared with one instrument, assuming you don't have equity constraints or a system that is always in the market. This means that there will be higher returns when trading two markets than with one market for a given bet size.

Mark Johnson posted some recent research findings on the Trader’s Club Forum where he illustrates that trading correlated futures markets gave better returns by a substantial margin than simply trading a smaller but more ideally diversified basket of markets. His insights into the reasons behind this strike me as true.

The results while more dramatic than I would have expected, do not surprise me. Richard Dennis’ research, and my subsequent research, also indicate that strong correlation should not be a reason to exclude markets from a trading basket. The benefits outlined above greatly outweigh the added risk of correlated drawdowns when considered across the entire basket.

For example, while it may seem riskier to trade Swiss Franc, Euros, and Japanese Yen than to trade just the Japanese Yen, that is not really what is being proposed. This decision is not taken in isolation.

The increased risk within one market group is more than offset by the greater opportunity to offset the added risk provided by the other additional markets Crude Oil, Natural Gas, Heating Oil, etc. So one can’t consider just the increased risk within a correlated group, but needs to also consider the mitigating effects of the increased diversification provided by expanding the breadth of other groups, which while they may correlate with each other, don’t correlate with the group in question.

The question remains, how does one use the power of diversification without losing too much return to the dillutive effects of trading weaker markets.

One approach is to take the route that the Turtle System uses which is to trade a basket of all liquid markets but to limit your risk in correlated positions on both a strongly correlated and weakly correlated basis. This has the effect of making sure that while you have the opportunity to trade any market that starts trending, you’ll confine your trading to the strongest markets within a correlated group. In some respects, this provides the benefits of diversification with less downside.

I’ve always thought that this was one of the overlooked features of the Turtle System that improved results but that had not been tested by others because it is hard to program. After reading Mark’s post and this thread, I decided to test this using VeriTrader™.

Our testing indicates that these correlation based risk limits increase risk-adjusted returns by a very significant margin. For example, consider two tests of the Turtle System using VeriTrader™ with a basket of 23 commodities (BO, BP, C, CC, CD, CL, FX, ED, GC, HG, HO, HU, JY, KC, MP, NG, S, SB, SF, SI, SM, US, and W) from Jan 1983 to Dec 2002. Test One uses the optimal correlation limits as outlined above. Test two uses only the single instrument limits and directional limits (i.e. only X short units and X long units). All other parameters were held constant for this test.

Results 1983 - 2002:

Test One – Correlation Limits
Return 49.3%
MAR 1.36
Max Drawdown 36.28%

Test Two – NO Correlation Limits
Return 48.3%
MAR 1.15
Max Drawdown 42.16%

The same tests run from 1993 to 2002 yield even more dramatic differences:

Test One – Correlation Limits
Return 41.5%
MAR 1.57
Max Drawdown 26.50%

Test Two – NO Correlation Limits
Return 39.1%
MAR 1.11
Max Drawdown 35.32%

Sometimes very interesting fruits lie beyond the edges of what can be easily tested.

P.S. I should mention that it took a lot longer to write the description of the test and the associated text of this post than it did to run the test itself. :wink:
Last edited by Forum Mgmnt on Tue Apr 29, 2003 1:43 pm, edited 1 time in total.
Sir G
Moderator
Moderator
Posts: 243
Joined: Wed Apr 16, 2003 12:21 am
Location: Salt Lake City, Utah

Post by Sir G »

BondTrader certainly taps into the point of self discovery, but let me offer a few things.

Kiwi:

Risk & opportunity live in the same world and we need to look at them both together as they impact each other. It’s like with position sizing, sometimes you will see the DD increase, let’s say by 15% but the annual return might increase by 35%. If you look at just the risk end of the scale, you will miss out on the benefit of the return. In this case you have bettered your risk adjusted return. And that is what it should be about, not the DD or the Return but the synergy of them both.

Also, let’s look at the concept that the markets only trend 15% of the time. This is also “market lore” that should be questioned and investigated. AMong other things, What is the definition of trend used in this statement?

But if you believe it to be a good estimate and that your system profits by exploiting these trends, doesn’t it make sense to load up when these trends occur? It's like a blacksmith you have to strike while the iron is hot.

Sir G
drm7
Roundtable Fellow
Roundtable Fellow
Posts: 96
Joined: Sun Apr 20, 2003 9:02 pm
Location: Richmond, VA

Response to c.f.' test - more thoughts about correlation

Post by drm7 »

This thread has turned into quite a discussion!

I have a question for c.f. about his test - Which Turtle System did you use for the correlation test, the 55/20, the 20/10 or a mix?

My take on correlation is that it doesn't matter as much until bad stuff happens, and you find yourself with triple and quadruple exposure to a "discontinuous event" (Taleb's 'Black Swan') I just finished Taleb's chapter about the emerging market bond trader who didn't think that Russia, Mexico and Brazil could possibly affect each other - until he blew up in 1998. In October 1987, almost all stocks dropped dramatically, wiping out traders with leveraged "diversified" positions.

Trading low correlated markets will provide some incremental value in "normal" circumstances, but will really protect you when everything goes to crap in a selected market group.
Forum Mgmnt
Roundtable Knight
Roundtable Knight
Posts: 1842
Joined: Tue Apr 15, 2003 11:02 am
Contact:

Post by Forum Mgmnt »

The test was run with a mix of short-term System One and long-term System Two. The exact parameter values differ from the rules but they are pretty close in most respects.

I don't consider a system as a static set of parameters like 20/10 or 55/20 but more of a concept that can work across many different values and timeframes.
Sir G
Moderator
Moderator
Posts: 243
Joined: Wed Apr 16, 2003 12:21 am
Location: Salt Lake City, Utah

Post by Sir G »

Hi forex_kid

A) Test your system with 2% risk per market 6% portfolio
B) Trade three markets, pencils, erasers, and scissors
C) Get three new buy signals and open a 2% position in each
I never heard those rules before. The rules that I like are there are no rights and wrongs just varying degrees of better and more fair. You need to create/apply your rules with the end result in mind. My rule helps me in that endeavor.

In your B you wrote:
  • B) Trade three markets, pencils, erasers, and scissors

I wonder if you are you a studious person? Why would you select those 3 for markets? Just as a gold bug will select gold, does this in anyway direct us to opportunity?

Maybe this month the markets that may offer the best opportunity are
  • Buffalo Wings
  • Beer
  • Potato chips
Let me ask you, how many system elements to your ABC rules do you see? The most likely answer is two, Entry and position size. But I see three elements.
  1. Portfolio Selection
  2. Entry
  3. Position Size.
If you break down the elements of the act of trading, perhaps the first three elements will be the ones above. Now if you look at each element as either Opportunity related or Risk related I would score it as such:
  1. Portfolio Selection =Opportunity
  2. Entry =Opportunity
  3. Position Size =Risk
Why would we not want to take advantage of an opportunity? I don’t like to view portfolio selection as simply the universe of markets that we follow or to let out entries dictate the selection by doing so, you completely miss out on an important step.

Is there a way we can let our markets ebb & flow with our systems, but we employ a way to select which markets we will trade. Just because an entry occurred in one market, might not mean on the grander scheme of things that it is equal opportunity. Have you ever broken down your year end statement to see what each market contributed? I’m sure you’ll find a handful made a ton, a handful lost a bunch and the 70% or so in the middle just kinda broke even. While each market might have represented the same degree of risk, did each market offer the same opportunity?
See: viewtopic.php?t=41
For a book on the 80/20 theory. Is there a way that we can exploit this?

Let's look at it like this, you have the opportunity to meet someone new and someone you have never met before. But you are allowed to only pick one person and you get to have a 2 hour lunch with this person. That is the opportunity.

You are then allowed to select a person from a pool of 10.

One person is Richard Dennis and the rest are randomly selected, a cop, a criminal, a priest, a gas station attendant and so on.

Who would you select?

While I will never argue that you can’t learn and enjoy everyone’s company, depending on your goals and desires you might find one more desirable then the others. Is there a way to apply that kind of selection to the portfolio?

Hopefully Food for thought.

Sir G
Post Reply