## Friday, January 8, 2010

### Calculating returns with little data

I'm spending most of this week on an assignment for a client who is engaged in a lawsuit; well, actually I'm doing the work for the client's attorney. I'm charged with calculating returns for the stocks in the portfolio, and was given only year-end statements that include the year-end positions, along with transactions, income, and disbursements for the year. The first year only has that year's ending position. The exercise spans six years. How does one do this?

I am calculating both time- and money-weighted returns. I'll therefore need monthly returns for the time-weighting. So, how would you do it?

Again, all you have are:
• year-end positions
• transactions for the year
• income for the year
• disbursements for the year.
I'll let you ponder this awhile before stating how I did it.

BTW, I think this would be a good exercise for the CIPM program!

1. Why returns when most likely the legal team would want to know the damanage in dollars (\$\$\$ and not %). Use the data you have and calculate (in your case guestimate) the yearly capital appreciation / depreciation. Once that is completed, calculate a P/L (not a return) and provide disclosure explaining the limiations and issues. Done complete!

2. You're confusing money- and time-weighting. Mangers can't control cash flows, therefore we use time-weighted methods. Granted, we (as well as others) argue for money-weighting at the subportfolio level because managers control these flows. I've only shown part of the assignment, as I'm not at liberty to disclose much more. Returns will demonstrate how the manager did.

3. Assume you have all the necessary transaction activities: you could recreate the portfolio return(s) in a performance system. I agree with your comment.

My pervious comment was related to your second comment. Let's assume a similar question was purposed in a CIPM exam, how would someone within 3 hours be able to recreate the portfolio history and calculate the portfolio return(s) without having all the necessary data?

By the way, that is a big assumption stating managers can't control cash flow. This is the major limitation when calculating a daily time weighted return. How do we know if a manager was controlling the flows without performing a cash reconciliation with the custodian?

4. I don't disagree that responding in a 3-hour exam might be a challenge, but someone should, I believe, be able to fairly quickly identify what they would need to do. Even if it was a multiple choice test where you were given the scenario and asked COULD you derive the returns and if not, what additional information would you require? I think this example is more of a "real world" situation that we've encountered a few times. Not sure all performance measurement professionals could figure out how to do it, though I suspect many could.

5. I believe the exam mainly focus on calculation process and not enough focus on data aggregation process to calculate the return. One taking or passed the exam would probably know how to calculate a return using various methods IF all relevant data is available. What is consider relevant? Not market values and total cash flows (if you're programmer you'll know what I'm taking about. Just a note, I'm not a programmer). In event a return problem does occur, I doubt many would know how or what to look for in the database full of journal / transaction entires and valuations (performance analysis is easily as long as you don't need to fix it). Oh, above is another reason why a verifier needs to visit the company.

My method is a simple P/L calculation without cash flow involvement (really just a quick and dirty method). Certainly, I doubt GIPS or a verifier would recommend this method, it probably could be used in an attribution calculation. Anyway, without going into details between you and your client, using just what stated above, what process would you take?

6. Your method seems a bit flawed, though I'd have to see more to really pass judgment.

Memorizing formulas is easy; understanding what's going on and how to work around it is the challenge.

7. If you have year-end positions and all the transactions (including dates and prices, I'm assuming), you could back into the monthly positions. The end of month/cash flow prices could come from anywhere (FactSet, Bloomberg, Google, etc.). That should be all the info you need. Plug that into a Modified Dietz template in Excel. That solves the TWR. For the MWR, you can create the beginning market value, and you have the ending market value and transactions/flows. I would use Excel's IRR formula or utilize it's Solver function to equate inflows and outflows.

8. As long as the assets are custodied and marked by an independent bank and not via a partnership (or similar) vehicle I'd say the needed information is available. # of shares, intra-year transaction dates (shares, price, costs), income and disbursement per security are publicly available against which to reconcile.

Things change depending on the investment vehicle, and presence of private equities (or SPV's used for accounting tricks).

Right?

9. You ARE correct, Derek! You win!!!
It's really not that hard, though it can be VERY time consuming, especially if there are corporate actions to consider.
Transactions should identify corporate actions (ideally).
Getting the prices shouldn't be difficult, as there are many sources for this.
We've developed automated ways to do this for clients, so it's not a challenge technically.

10. I disagree with Derek / Dave's opinion on using TWR when there is a distribution within the month. Maybe, depending on the timing of the flow, Modified BAI is probably a better choose.

My comments are just my assumptions since I don't know the details of the system that Dave Mentioned. The system needs to some how determine if the transactions should have a direct or indirect impact to the portfolio market value (for example, bank fee - should we treate this as a flow? My favorite, miscellaneious transaction, what is it and how should performance treat this transactions?). For internatinal portfolio, it could get a little more challenging (1 issue, fx rate use for repatriation).

Yes, most websites provide pricing information. However, we should use correct valuation (with correct corporate action) from either Bloomberg or Factset and not free websites. If a return relying on the transaction statement (most likely a settlement date statement), the dividend would not appear until it settles. thus the return is not calculated using trade date information (unless Dave's system recognizes this, but there are other things to look at as well. Fixed income gets more challengeing because of security modeling). Sorry, I'm not going into details with derivatives or private equities (my hands would drop).

No system is perfect and I still believe human judgment / experience is needed when calculating return. Fixing or recreating return is like tryign to find a needle in a haystack.

11. Mod BAI essentially equals Mod Dietz, so no real benefit there.

Your transaction file should include all the results of corporate actions, so you won't lose anything (except possibly stock splits, which your pricing vendor should reflect). Your transaction file should reflect spinoffs, etc. But all valid points suggesting that care is important to ensure you end up with good information.

12. The reason why I'm purposely commenting on this is that I feel too many practitioners / consultants / verifiers / managers (and others) think performance calculation function is an easily task. Hopefully someday these people would think differently.

Modified Dietz is similar to Modified BAI. Modified BAI is similar to daily time weighted. Daily time weighted is similar to True time weighted. All fo these equations are similar and all have some form of limitation(s). Especailly, daily time weighted and true time weighted is more dangerous than the other methods because a user could "game" or play around the results without changing from either beginning or end of the day calculation.

If you referring to a flat file, then it'll not show you details of the corporate action activities. If you referrring to a statement, then the reconciliation team needs a settlement date statement to insure all cash activities settles. When you calculate performance, you'll need trading date activities statement so performance could be calculated using trade date.

13. Perhaps its semantics, but I would suggest that:
1) Mod Dietz and Mod BAI are equivalent
2) Both Mod Dietz & Mod BAI time-weight daily (rather than mid-period)
3) Mod Dietz and Mod BAI should give the same results
4) Mod Dietz and Mod BAI approximate Exact (or true) when cash flows are relatively small.

With the transaction details, you can employ any model as long as you can get the prices.

14. As long as you have securities that are prices, you can have a return or a number. However, the main differences on all these methods is related to the treatment of cash flow. Take cash flow out and in theory the results MUST be identical. Add cash flow into the picture and the results will differ. What if someone plays around with the cash flow. The return or that number WILL change. How do you know if the cash flow isn't being play around.

15. Cash flow is probably the only transaction that could be used in daily or true time weighted return that will impact the return and not leave behind any brakes. Any adjustments to the accounting / data / valuation could window dress the return but will evenually cause break(s) or be readjust back in the following month. Are the verifier / practitioner aware of this limitation?

16. At the portfolio level, cash flows are the only transactions we care about from a return perspective (other transactions come into play when we do subportfolio returns). As to verifier knowledge, I think it depends on which one you speak with.

17. For performance calculate using daily time weighted method: Cash flow (I meant new money that is not control by the portfolio manager). If at the portfolio level you can game the return, you can also duplicate the same effect at the sub level. Depending on the setup, the sub level could have more issues because you'll need to factor in the cash flow movement (this time is the money movement decision from either the client / firm itself / portfolio manager decision).

In simple accounting 101, everything flows through cash ledger. If anyone was to manipulate other cash flow activities, it could have an immidate or direct impact to market value. However, these activities will casue a break when someone was to work on a daily cash / market value reconciliation. Thus, this is something that could easily be spotted if there is simple control in place.

The limitation on daily time weighted is by using posting a cash flow in one day and out the next when the portfolio experience high level of market value change. Because the flows are going in and out, the month end reconciliation will have 0 impact to ending cash flow and market value. However, because you're adjust the the market values at the time of heavy market value movement, the performance using daily time weigthed is effected. If you use Modified Dietz, this method will not work and the equation will probably give you a more accurate result. However, Modified Dietz has its own limitation.

18. Your points aren't limited to the scenario as originally proposed but to returns in general. Essentially, if firms want to "game" returns, they can, until the SEC conducts a thorough review or, if they're a GIPS compliant firm, they're verified.

19. I got side track on my ideas. Just to note, I never seen the method I discrible being use in a performance calculation. However, now that readers know of this limitation of using daily time weighted method, will Verifiers / Managers continue to claim daily time weighted is more accruate? Maybe, performance calculation is a simple job function? Hopefully, the industry would change the preception. Thanks for posting my comments.