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January 12, 2007

A Tale of Two Money Managers

I happen to have two accounts at my friendly neighborhood long-short, highly-leveraged, growth-focused, discretionary money management firm. Like your typical brokerage, my accounts are each managed by a single individual with his own ideas, prerogative, and strategy. Unlike your typical brokerage, they trade stocks for me without asking, and quite aggressively at that. In some respects, it amounts to a hedge fund for us little folk. How well do they do? See for yourself:

Account Date Opened Returns To Date* S&P 500 on same interval Russell 2K** on same interval
Money Manager 1 Mar, 2003 155.21% 64.31% 113.55%
Money Manager 2 Sep, 2005 56.67% 15.38% 17.96%

* After all fees, but not including tax consequences

** Rather than the S&P, these managers benchmark themselves against the Russell 2000, an index of small-cap equities

Both have done substantially better than the market, but could it be just because they trade on margin and the markets have been up? That is, how do you isolate the component of success attributable to the investment strategy, as opposed to just amplifying the swings of the market? For now, we will focus on one account, the one that has been open the longest:

Money Manager 1 (MM1) certainly tracks the indices in general, but there are points (eg August 2006) at which he goes up then the market goes down. As my homey JDiggitl suggests, it is possible to get a handle on this by plotting my account's monthly returns against the returns of an index over the same period of time. Do a linear regression on this, and the y-intercept suggests the expected returns when the market is flat:

The slope of the linear fit [sorta] represents the degree do which his portfolio correlates with the market. In both cases the slope is less than one because of a substantial number of short positions, but regardless he is expected to return 1.2% points better than the market. Not so shabby -- in 3.75 years he has turned $1,000 (for the sake of this discussion) into $2,552 (total) where the S&P would have only given me $1,643 and the Russell $2,136. I'll take it. I'm glad these guys make hundreds of thousands of dollars per year.


But wasn't this a tale of two money managers? I want to compare them, but it can be difficult because one account is almost four years old, the other less than 18 months. The best I can think of is, from here on out, to only use the data for Money Manager 1 (MM1) over the time period in which I have also had an account with Money Manager 2 (MM2). The basics:

AccountReturns
Money Manager 141.47%
Money Manager 256.67%
S&P 50015.38%
Russell 200017.96%

So far, Money Manager 2 is winning out. What about those scatter plots?

Money Manager 2 has a larger overall return, and while they are similarly correlated with each of the indices, MM2 can be expected to do about 0.7 percentage points better than MM1 when the market is flat. To augment this analysis, we can also apply some of the standard metrics for comparing money managers. The below table is a summary of calculations from the excel spreadsheet from whence all this analysis flows.

 Money Manager 2Money Manager 1 (since 9/05)
Avg Monthly Return3.09%2.43%
Stddev Monthly Return0.0330.045
Risk Free Rate*0.41%
Total Months15
Total Risk Free Return6.29%
Beta (vs Russell 2K)**0.6060.640
Beta (vs S&P 500)**0.9911.034
Sharpe Ratio0.9300.544
Jensen's Alpha (vs. Russell 2K)43.31%23.11%
Jensen's Alpha (vs. S&P 500)41.38%25.78%

* Assumed 5% year (i.e T-Bills), monthly rate
** note how close these Beta's are to the slopes of the linear fits above

Every metric, from absolute percentage returns to the basic measurements of portfolio theory suggest that Money Manager 2 is better than Money Manager 1. Sharpe Ratio is only to be used as an ordinal comparator, but I believe that Jensen's Alpha actually quantifies the excess returns that can be attributed to the smarts (or luck) of that particular investor's strategy.

Do I take my whole account from MM1 and give it all to MM2? Transaction costs aside, this analysis would suggest that I should, but it's hard to call up a guy who has more than doubled my money while I slept and tell him that. Regardless, I have benefited a lot from access to these smart and hard-working investors. If I'm really lucky, they will outpace the New York Real Estate market and one day I might get to live in the same neighborhood I grew up in.

We all know that past performance is no guarantee of future results, but if you have $10,000 and want to take a chance, let me know. They only take clients by referrals.

Update, 8 months later (12/07 to 8/07, over which time the the S&P and Russel 2000 are up 2.49% and 1.4%, respectively):

Account Returns Since 12/06 Total Returns To Date
Money Manager 1 8.59% 177.13%
Money Manager 2 5.68% 65.57%

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