Tracking Error Management & Sources of Return and Risk

When it comes to passive investing, the goal is simple: match the underlying benchmark index. What do you think is the best way to measure passive management success?

Take a look at both equations. Although they may seem similar, tracking error and excess returns are different and not interchangeable. As an example, looking at the equations, which one can't be negative?

Incorrect. Management fees are a good data point to evaluate but not the best way to measure success.

No. Liquidity of the fund doesn't measure the benchmark index versus the portfolio.

No. Excess returns can be negative.

That's right!

Since an outside manager is involved in creating the passive portfolio, what additional cost might increase tracking error?

No. There are limited costs associated with any withdrawals, and most times, there's actually no cost.

When might a cash drag be positive for excess returns?

Incorrect. Passive investment minimums are usually very low, so there's no associated cost here.

Not quite. If the market is flat, then the cash is earning roughly the same return.

Incorrect. When the market is rising, uninvested cash will hurt excess returns.

That's right! When the market's going down, a cash drag actually helps excess returns by increasing the portfolio's return in comparison to the benchmark return. But while this is a benefit, it's not the mandate of the investment manager. Passive portfolio managers must weigh the benefits and costs of maintaining a minimal tracking error. For this reason, most managers aim to keep the portfolio's beta at 1.0 in relation to the benchmark index. Speaking of trade-offs, when it comes to passive strategies, it's still important to analyze returns and risks associated with passive investments. For returns, managers can perform attribution analysis by segmenting the benchmark and portfolio into sectors and then identifying the return attribution as the difference between the sector return times the portfolio weight less the sector return times the benchmark weight. This helps the manager understand the sources of return.

How might the investor and agent earn additional low-volatility income?

For these reasons, borrowers tend to prefer institutional investors like mutual funds or pension funds because they're unlikely to claim the shares back suddenly. How might you describe this type of investor?

Incorrect. High-growth equities are volatile, which increases the risk of securities lending.

No. Foreign-exchange markets are volatile, so this increases the risk associated with securities lending.

Yes! Mutual funds and pension funds are long-term investors who make great lenders because they're unlikely to call the borrowed shares randomly. And, although the borrower must pay back dividends received to the lender, the borrower does get legal title to the securities and voting rights, which can be important for activism efforts. And when it comes to activism, institutional passive equity investors are usually amongst the largest holders of equity companies. These funds can have an enormous impact on corporate elections and the proxy outcome, which can lead to return-generating results. Plus, since most passive investors are long-term holders, passive activism can potentially lead to greater management efficiency. Potential issues include costs of voting proxies, potential conflicts of interest, and the effectiveness of passive equity activism.

Incorrect. Mutual funds and pension funds invest on behalf of their investors and beneficiaries, many of whom have decades until retirement.

Clearly, no. Pension funds and mutual funds aren't day trading.

To summarize: [[summary]]

Correct! As you know, tracking error measures the difference between the benchmark and the portfolio. It's calculated as the standard deviation of the differences between the portfolio return and its benchmark index return. >$$\mbox{Tracking error}_p = \sqrt{\mbox{Variance}_{R_p - R_b}}$$ where $$R_p$$ is the return of the portfolio and $$R_b$$ is the return of the benchmark Additionally, analysts also use excess returns, which measure the difference between the portfolio returns and benchmark returns. Its equation is as follows: >$$\mbox{Excess returns}_p = R_p - R_b$$.

Clearly, yes. Management and trading fees will increase tracking error because the benchmark index doesn't have fees in comparison. Likewise, the cost of brokerage commissions also increases tracking error. Intraday trading can also increase tracking error through managers trying to time the addition or deletion of securities in the portfolio. Another tracking error factor is the cash drag, which occurs when the portfolio has excess cash that's not invested in replicating the index. This can increase tracking error due to the lack of investment, which is why some managers use futures contracts to obtain exposure. Yet, the cash drag isn't always a negative when it comes to excess returns.

Right! The investor and lender can share in the additional interest income earned by investing in the risk-free rate. This has the potential to help passive investors earn additional returns. However, there are some risks, namely the credit quality of the borrower and the value of the posted collateral. Plus, the lender can take additional risk by investing the cash collateral in other securities.

Tracking error can only be presented as a non-negative number because it uses the variance of the difference between the returns. So even if a portfolio exactly matches the index from a total return perspective, the tracking error can still be positive if there are differences in returns over multiple periods. Clearly, a manager's ultimate goal would be to have a low tracking error and positive excess returns. But the higher the number of securities within the benchmark index, or the less liquid the underlying constituents are, or the less frequency of data updating, the higher the tracking error usually goes—that's not to mention another primary cause of tracking error from the manager's perspective.

Another source of return is securities lending, which (when successful) can actually lead the portfolio to make net expenses negative. This works by using a lending agent, who makes the investor sign a securities lending agreement and a master securities lending agreement. Essentially, the lending investor gives the lending agent the power to find a borrower, evaluate the collateral the borrower puts up, and split the fee paid by the borrower (usually 2%–10%, depending upon the borrower's credit quality and the security borrowed). When the collateral is other securities, the agent holds the shares as a guarantee. But when the collateral is cash, there's the potential for the lending investor and the agent to earn additional income.

Tracking error

Management fees

Fund liquidity

Excess returns

Tracking error

Withdrawal requirements

Passive investment minimums

Management and trading fees

When the market is flat

When the market is rising

When the market is falling

By investing the cash in the risk-free rate

By investing the cash in high-growth equities

By trading the cash in the foreign-exchange market

Long term

Short term

Day trading

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