Monday, September 19, 2011

What are the risk statistics for IRR?

Someone recently asked me what risk statistics should be used with the internal rate of return (IRR), (which, as any reader of this blog knows, is my preferred return measure). Sadly, I didn't have an immediate reply.

The plethora of risk statistics that are available for time-weighted rates of return (TWRR) use the intra-period returns. For example:
  • standard deviation (we can continue its appropriateness as a risk statistic)
  • beta
  • tracking error
  • downside deviation
as well as the multitude of risk-adjusted return measures that use these risk measures (such as Sharpe ratio).

Recall that the IRR measures the return for a single period; there is no linking. Comparing the portfolio's IRR with the benchmark's only serves the purpose of seeing how well the portfolio did. But how can we measure risk if we use the IRR?

Reflect on this for a bit;  I will return to this matter soon, with some concrete ideas.

3 comments:

  1. There are two scenarios where IRR is the more representative and relevant measure of performance: a) the manager controls the external cash flows (making these discretionary cash flows part of the investment process and b) the cash flows are part of the client’s financial goals (such as an endowment which needs to make contributions to its beneficiary organization each quarter.) This second scenario is very common for non-profit organizations such as foundations and endowments, and for pension plans. Equally important is its relevance for individual investors, especially high net worth investors who have a series of planned expenditures as the purpose of the portfolio. So, if we need a single measure of return for these investors, it’s the return of the portfolio through IRR.

    That said, what is the set of relevant risk measure(s) for these investors? Since their financial goals are related to the adequacy of the cash outflows and the preservation of portfolio value relative to targets, then I suggest that the risk around meeting these goals is the right risk measure. For example, funding ratio is the key risk metric for pensions – it doesn’t matter if your portfolio beat its asset benchmark if its funding ratio declined. That would be a failure, not a success. The volatility of return around an asset benchmark might be interesting to a performance analyst, but it is almost completely irrelevant to the client’s financial goal. Why measure the wrong thing with great precision? That would be precisely wrong. Similarly, a foundation portfolio needs to meet its grant making targets for its beneficiary organizations while preserving the value of the portfolio so that it can continue making these grants. The volatility of this cash flow relative to target is a relevant risk measure for this first client goal. The median portfolio value relative to its target value with a minimum and maximum value over the performance period are adequate measures of meeting this second client goal.

    You’ll note that these measures of risk have more to do with the adequacy of money rather than with return. This may sound like heresy to the fundamentalists of the performance world, but these illustrate the simplicity and clarity which emerge when we first consider the question we are answering, rather then simply rushing to calculate returns simply because that’s the comfort zone for people who like math and who work for fund managers. Can we create somewhat comparable risk measures around the money rather than the returns? I think we can. Tracking error? We can measure the tracking of the withdrawals supported by the portfolio compared with the planned withdrawals. Downside risk? We can evaluate the funding ratio of the portfolio relative to its minimum acceptable money value. Standard deviation? How about the standard deviation of both funding and portfolio value relative to their average values over a long time period? These all work from the money that is most relevant to the clients who own these portfolios.

    An IRR is a return that is defined by its consideration of money over the performance period. The risk inherent in an IRR should be calculated with an equal emphasis on money.

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  2. Steve, thanks for your comments. Tracking error requires a standard deviation of excess returns, which obviously therefore mean multiple excess returns being derived (these are usually done through time-weighting). Since IRR is across a full period, we have but one return for the portfolio and one for the benchmark. If we elect to calculate IRRs for the periods in between, then this approaches the TWRR; not that this would make such a risk measure inappropriate, though it does shift away from the IRR itself. Downside risk, too, requires multiple returns to be calculated.

    I don't disagree that including analysis of "the money" is appropriate, but getting down to the details is necessary to ensure that these approaches will work as we would hope. Thanks for moving this further along.

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  3. Stephen Campisi - The Voice of the ClientSeptember 24, 2011 at 3:52 PM

    Dave:

    I think you miss the point. Investors don't invest to get returns; they invest to get money. If you had a choice between a return that ignored your money needs and a return that recognized the money you need from the portfolio to meet your financial goals, I think we would both agree that the return that includes your money goals would be the more appropriate one. That would be the IRR. So far so good.

    If you had a choice between returns and NO information about whether you met your financial goals (which are MONEY goals) or information about whether you met your goals but NO RETURNS, then I HOPE you would choose the money information rather than the return information. Remember, we invest to get enough MONEY to meet MONEY-BASED financial goals. We DON'T invest to get returns. So, your statement that "I don't disagree that including analysis of "the money" is appropriate" is rather like telling a drowning man that you agree that throwing him a life preserver is appropriate, but you first have to check the statistical evidence that the rope meets industry standards, while the poor bugger sinks beneath the waves!

    It's the money that counts. The returns are simply an extrapolation from the money. The IRR is simply a number to represent the money success or failure in relative terms. You don't need to check the single period returns or the periodic returns to see if the money you withdrew from your portfolio was equal to or greater than your goal, and you don't need any fancy analysis to see whether your portfolio maintained its inflation adjusted value.

    As to risk: no one really cares about statistical measures of risk, because these say nothing about true risk to an investor: are you likely to fail to meet your money goal? The point is that the true measure of risk is in terms of money, not return. It's true that a higher IRR than a similar goals based IRR probably indicates success in meeting a client's goals, it does not necessarily do so. For example, exceeding your cash withdrawal goals in the beginning and then failing to meet them towards the end can still create an equivalent IRR as the goal. So in the end, you have to look at the money over time. If you do, you'll have a clear demonstration of success or failure.

    We'll know that we understand our clients' goals when we are ready to put returns analysis where it belongs - at the back of the bus as an interesting theoretical relative-basis analysis - but not a measure of success... unless you're selling a mutual fund.

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