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Practice Notes

Our experts write short one-page educational materials on important and relevant financial and statistical topics.

Sharpe Ratio

We provide a detailed discussion of the relationship between the underlying return distribution and the Sharpe ratio from a series of historical returns drawn from that return distribution. We provide two examples of portfolio allocations that highlight the importance of knowing the uncertainty in the measurement of the Sharpe ratio from a series of historical returns.

Malliavin Calculus in Calculating Delta for Structured Products

Malliavin Calculus, also known as Stochastic Calculus of Variations, is useful for calculating sensitivities of financial derivatives to a change in its underlying parameters, such as Delta, Vega, and Gamma. In this article, we discuss how to use Malliavin Calculus to calculate Delta for structured products.

Bid-Rigging Schemes in Securities Markets

Bid-rigging is an illegal agreement among conspirators in an auction to predetermine the winning bidder. News that the DOJ and the SEC are investigating bid-rigging schemes in the municipal securities market should not come as a surprise. Bid-rigging conspirators in variety of markets have used the same basic strategies to generate illicit profits for decades. Their actions cause measurable harm to the issuers of the securities involved.

Fee-Based Brokerage Accounts

Fee-based accounts do not eliminate all the conflicts of interest inherent in commission-based accounts. While fee-based accounts reduce an unscrupulous broker's incentive to excessively trade ("churn") an account to generate commission income, serious conflicts of interest remain.

Equity-Indexed Annuities: Toxic Investments

Equity-indexed annuities ("EIAs") are contracts with insurance companies that pay investors part of the capital appreciation in a stock index and guarantee a minimum return if the contract is held to maturity. The net result of EIAs' complex formulas and hidden costs is that they survive as the most confiscatory investments sold to retail investors. For an example of misleading EIA descriptions, see the attached Legg Mason page printed off their website today.

Asset Allocation

Studies have shown over 90% of the variation in historical returns to managed portfolios can be explained by variations in their asset allocation. Asset allocation recommendations, especially to investors living of their wealth should include analysis of risk over the investor's entire expected life.

Monte Carlo Simulation

Monte Carlo simulation is a powerful tool for estimating the risk of investments. The simulations can be set up in Excel spreadsheets and the assumptions varied to determine the impact of alternative decisions on the client\'s objectives.

The Fallacy of Time Diversification

Time diversification is the belief that risk declines over longer investment horizons because there is more time for future good years to offset bad years. Time diversification is a fallacy. But since remaining future earnings decline relative to our investments, we should hold less stock in our portfolios as we age.

Not Your Father's Utility Stock: When It's Not Just A Name Change

In the late 1990s, many publicly traded firms used their stock to buy up other firms. Exchanging a conservative stock for a speculative stock can dramatically increase the risk in an account. Financial advisors must recognize this material event.


Beta is a statistic developed from the Capital Asset Pricing Model ("CAPM"). Beta is typically misused whenever it is offered as a measure of risk, significantly understating the risk relevant to most retail investors. Investors as a general rule should therefore not use beta to measure risk.

Standard Deviation, Sigma or s

Standard deviation is the correct measure of risk for investors' entire portfolios. Presentations of standard deviation can be tailored to inform investors of varying levels of sophistication. It is simple to calculate and interpret and is ubiquitous in the investment management literature and in the brokerage industry.

The "Issuer Fraud" Defense in Securities Arbitration

Respondents sometimes attempt to shift blame for losses in retail accounts to issuer fraud at companies like WorldCom and Enron. Finding an investor's portfolio imprudently concentrated, arbitrators must not care whether the risk materialized was of an accounting fraud, discovery of a toxic dump or the failure of a bet-the-ranch strategy.

Covered Call Options & Hedging

Brokers sometimes recommend that investors holding concentrated stock positions sell call options against their stock to hedge risk. Often sold as a conservative strategy, covered call writing delivers exactly the opposite.

Covered Call Options & Income

Brokerage firms sometimes recommend that clients sell call options to generate income from concentrated positions. Investors, who hold concentrated positions, in part in reliance on the industry's misleading descriptions of covered call writing, may continue to be imprudently exposed to substantial diversifiable risk.

GMDB's Are Not Much of a Benefit

Annuity abuses arise if investors are misled into believing that the guaranteed minimum death feature of an annuity is worth anything more than a de minimis amount.

Tax Deferred Annuities Can Make Investors Poorer

Tax deferred annuities often leave investors with less after-tax wealth than they would have had in a taxable account.

Out-of-Pocket Losses in Stock Option Arbitrations

Out-of-pocket losses are miscalculated in employee stock option arbitrations when stock received is valued at the options' strike price.

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