Archive for the 'Performance Measurement' Category

Risk Adjusted Return Measures: Ex-Post Jensen’s Alpha

On an ex-post basis, performance can be appraised by using the Security Market Line (SML) as a performance benchmark. The difference between the account’s performance and the risk free rate would then equal the sum of:

  1. Manager’s alpha
  2. The product of the manager’s beta and the market risk premium
  3. Random error

Manager alpha is the return generated in excess of what “should have” been generated, given the level of risk taken.

Posted on 7th April 2008
Under: Active Management, Investment Returns, Performance Measurement, Portfolio Management | 1 Comment »

Price Weighted Index

A price weighted index such as the Dow Jones Industrial Average represents the arithmetic mean of the prices of each security in the index.

The Dow Jones Industrial Average is calculated by adding up the prices of each stock in the index, then dividing the total by a divisor, which is an adjustment to reflect the impact of stock splits, dividends and changes in the index components over time.

In a price weighted index, returns are influenced by the stocks trading at the highest price. A stock trading at $100 will have twice as much impact on the index return as will a stock trading at $50.

Posted on 2nd April 2008
Under: Investing in Stocks, Passive Management, Performance Measurement, Portfolio Management | No Comments »

Prime Brokers

This article was originally written by Richard Wilson in his Hedge Fund Blog.

Prime Broker Definition
A large bank or securities firm that provides various administrative, back-office and financing services to hedge funds and other professional investors. Prime brokers can provide a wide variety of services, including trade reconciliation clearing and settlement, custody services, risk management, margin financing, securities lending for the purpose of carrying out short sales, record keeping, and investor reporting. A prime brokerage relationship doesn’t preclude hedge funds from carrying out trades with other brokers, or even employing others as prime brokers. To compete for business, some prime brokers act as incubators for funds, providing office space and services to help new fund managers get off the ground.

Posted on 13th March 2008
Under: Hedge Funds, Performance Measurement, Risk Management, Trading Execution | No Comments »

Compound Annual Growth Rate (CAGR)

The compound annual growth rate is a number that represents a steady level of growth from a beginning value to an ending value. It can be thought of as a way to smooth out uneven returns.

To calculate the CAGR of an investment over a period of n years, you would take the nth root of the total percentage return.

Consider a beginning investment of $100 and an ending investment of $161. 161/100 = 1.61. The fifth root of 1.61 is equivalent to 1.61 to the power of 1/5, or 1.1. Subtracting 1 (100% or the initial investment) gives 0.1, or 10%. The CAGR in this case is 10%.

Since the CAGR smooths out uneven returns, it fails to account for the risks taken to achieve the return.  Any series of returns that starts at 100% and ends at 161% five years later will have a 10% CAGR, such as the investments in column A and Column B below.



     100.0      100.0
     110.0      150.0


     121.0      120.0


     133.1      170.0


     146.4      130.0


     161.1      161.1


Column A actually grew at 10% per year. Column B had large positive gains in some years and large negative gains in others, but ended at the same value. Many investors would prefer the investment in Column A due to its greater predictability and equivalent terminal value.

Posted on 12th March 2008
Under: Fundamental Analysis, Investing in Stocks, Performance Measurement | No Comments »

Presenting Composite Returns Under Global Investment Performance Standards (GIPS)

A composite is a combined account composed of similar portfolios. Composite return is the asset-weighted average return of the individual portfolios in the composite. It must reflect beginning-of-period values and any external cash flows. Each external cash flow is weighted according to the percentage of time held in the portfolio during the measurement period.

Under GIPS, all fee-paying portfolios must be included in at least one composite in order to prevent poorly performing accounts from being excluded. Non-fee paying portfolios can be included if this is appropriately disclosed. Non-discretionary portfolios, however, cannot be included in a composite. A portfolio is considered discretionary if the manager is able to implement the intended strategy. When clients impose restrictions or make frequent external cash flows that impede the investment process, the resulting performance may not accurately reflect the manager’s investment ability.

Posted on 9th March 2008
Under: Investment Returns, Performance Measurement, Portfolio Management | No Comments »

Micro Performance Attribution: Fundamental Factor Model

Micro performance attribution can help determine the sources of return generated by a particular active portfolio manager. Virtually all micro performance attributions involve a factor model. Some such models are limited to economic sectors and industries, and compare the return due to sector selection with that due to security selection within the sector.

Other factor models can include a variety of factors, including:

  • Size
  • Growth characteristics
  • Valuation
  • Financial strenth

Posted on 7th March 2008
Under: Active Management, Investment Returns, Performance Measurement, Portfolio Management | No Comments »

Combination Hedges

Financial futures markets typically use one instrument to hedge a position. For example, a 10-year note future might be used to hedge a position in 10-year Treasury securities. However, such hedges can often be imperfect due to the structure of futures markets. A futures position can be satisfied by delivery of a wide range of bonds, and the cheapest to deliver (CTD) option may have qualities that differ significantly from the bond being hedged.

In the January/February 2008 Financial Analysts Journal, Lawrence Morgan addresses this issue and provides an example: in February 2007, the 10-year T-note was yielding 4.625%, but the CTD for the June 2007 10-year note futures was the 4.25% November 2013 note – a 7 year instrument.

Morgan examines whether combination hedges, made by combining two hedging instruments, would provide a better match. Leschhorn (2001) developed and tested an approach for the German bond market in which the weights of the two hedging instruments were determined by their yield differentials. Morgan notes that this approach can frequently result in unstable hedge ratios.

Morgan extends the analysis to combination hedges weighted by option-adjusted and non-option adjusted modified durations, and finds that in general option-adjusted modified duration weighted combination hedges performed best.

Posted on 5th March 2008
Under: Active Management, Derivatives, Fixed income investments, Futures, Hedge Funds, Investing in bonds, Investment Returns, Performance Measurement, Risk Management | No Comments »

How Value and Growth Stocks Deliver Returns to Investors

In the November/December 2007 Financial Analysts Jounal Fama and French break down the returns historically delivered by growth and value stocks into dividends and three components of capital gain: growth in book value, primarily through retained earnings; convergence in price/book ratios due to mean reversion in profitability and expected returns; and the general upward drift in P/B ratios experienced over the last century.

For value stocks, the capital gains arise primarily from convergence. P/B reverts to the mean (increases) and many of the companies that were cheap due to lack of profitability become more profitable.

For growth stocks, the growth in book value is the primary positive factor for returns and convergence is a negative one.

Drift has had a negligible effect on average returns, regardless of the growth or value profile.

Posted on 17th February 2008
Under: Active Management, Fundamental Analysis, Institutional Investing, Investing in Stocks, Performance Measurement, Portfolio Management, Research, Security Selection, Valuation | No Comments »

Calculating Portfolio Returns Under Global Investment Performance Standards (GIPS)

GIPS requires portfolio returns to be calculated using time-weighted total return, adjusted for external cash flows. Portfolios must be valued for return calculations at least monthly (beginning in January 2010 valuation must occur at least monthly on the last business day of the month and also whenever large external cash flows occur.)

The definition of a “large” external cash flow must be applied consistently. Firms can formulate and document composite-specific policies as long as the policies are consistently applied. The policy must describe the methodology for computing time-weighted return (beginning in January 2010 only true time-weighted return will be permitted) and the assumptions made regarding capital inflows and outflows.

Posted on 9th February 2008
Under: Investment Returns, Performance Measurement, Portfolio Management | No Comments »

Macro Performance Attribution

Macro attribution analysis is conducted at the level of the fund sponsor rather than the portfolio manager. The distinction relates not to who conducts the analysis, but to the factors considered.

Macro attribution can be expressed either as a rate of return or as a value. It expresses total return in terms of:

  • The policy allocation to each asset class
  • The benchmark portfolio return for each asset class
  • The returns, valuations and external cash flows related to each manager hired

Macro performance attribution decomposes the change in portfolio value into a variety of components, which can include:

  • Net contributions – how much of the change in value was due to additions and withdrawals from the portfolio
  • Risk-free asset – the return that would be generated if the fund and all contributions were invested at the risk free rate
  • Asset categories – the return that would be earned on passive investments at the policy weight for each asset class
  • Benchmarks – the difference between the sum of the weighted returns of manager benchmarks and the asset category return
  • Investment managers – the difference between the weighted average sum of manager returns and that of their benchmarks
  • Allocation effects – this category reconciles the difference between the fund’s actual return and the separate analyses conducted above, in order to account for any differences resulting from deviation from policy weights

Posted on 7th February 2008
Under: Active Management, Institutional Investing, Investment Returns, Performance Measurement, Portfolio Management | No Comments »