Tuesday, March 22, 2005

SSRN-Sharpening Sharpe Ratios by William Goetzmann, Jonathan Ingersoll, Matthew Spiegel, Ivo Welch

SSRN-Sharpening Sharpe Ratios by William Goetzmann, Jonathan Ingersoll, Matthew Spiegel, Ivo Welch

Measuring fund manager performance is not as easy as it sounds. Sure you know the basic measures: Sharpe Ratio, Treynor measure, and Jensen's alpha.
Sharpe: (Return-Risk Free)/ Standard Deviation
Treynor: ( Return-Risk Free)/ Beta)
Jensen's Alpha: Return = RF + Beta (Market Risk Premium) + Alpha
But each measure has its problems. For instance as far back as the early 1980s, financial economists (including Henricksson and Merton 1981) showed that the Sharpe Ratio could be a poor measure in the presence of "non-linear payoffs".

There really has been no good solution to this. Indeed in Robert Strong's Portfolio Construction, Management, and Construction Text, he concludes a discussion on the topic with a true, but unsatisfying statement:
"We have numerous analytical tools and we have a brain; we should use both in evaluating the performance of a portfolio."
In Sharpening Sharpe Ratios, William Goetzmann, Jonathan Ingersoll, Matthew Spiegel, and Ivo Welch discuss the problems of the traditional performance appraisal methods and show that this is particulary troubling with the widespread use of derivatives (because their payoffs are inherently non-linear).

The paper then shows how these biases can be "gamed" by fund managers using options to take advantage of the limitations of the Sharpe Ratio. Once this is established, the authors develop a "manipulation-free" measure.

While on simplicity grounds alone, I doubt the new measure will be a big hit in undergrad classes, it definitely addresses the key attributes that a new measure should have. To understand the derivation, I recommend you read the paper. :) I tried to copy the equation in (equation 30) but I could not paste it and have top get to class now...sorry...



Suggested Citation
Goetzmann, William N., Ingersoll, Jonathan E., Spiegel, Matthew I. and Welch, Ivo, "Sharpening Sharpe Ratios" (November 2004). Yale ICF Working Paper No. 02-08; AFA 2003 Washington, DC Meetings. http://ssrn.com/abstract=302815

2 comments:

The Assetman said...

Nice paper and nice posting, professor! Keep up the great work...

deon said...

Hi

Tks very much for post:

I like it and hope that you continue posting.

Let me show other source that may be good for community.

Source: Performance appraisal methods

Best rgs
David