Portfolio Management

inter-temporal rate of substitution

represents an investor's trade-off between real consumption now and real consumption in the future

Shiller's CAPE (real cyclically adjusted P/E)

reduces the volatility of unadjusted P/E ratios by using real (i.e., inflation-adjusted) prices in the numerator and a 10-year moving average of real earnings in the denominator.

Commercial real estate characteristics`

• Bond-like characteristics. The steady rental income stream is similar to cash flows from a portfolio of bonds. Furthermore, just as the credit quality of issuers affects the value of a bond portfolio, the credit quality of tenants affects the value of commercial real estate.

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• Equity-like characteristics. The value of commercial real estate is influenced by many factors, including the state of the economy, the demand for rental properties, and property location. Uncertainty about the value of the property at the end of the lease term gives commercial properties an equity-like character.

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• Illiquidity. Real estate as an asset class is characterized by illiquidity; it could take years to exit a real estate investment at its fair value.

closet index fund

A closet index fund is a fund that is purported to be actively managed but in reality closely tracks the underlying benchmark index. These funds will have a Sharpe ratio similar to that of the benchmark index, a very low information ratio, and little active risk. After fees, the information ratio of a closet index fund is often negative.

What is the information ratio of a market-neutral long-short equity fund?

It equals the fund's Sharpe ratio — because with zero systematic risk and the risk-free rate as benchmark, active return equals portfolio return minus the risk-free rate, and active risk equals total risk, making the IR and Sharpe ratio calculations identical.

How does tripling the active weights of an unconstrained portfolio affect its information ratio?

It doesn't change the IR — both active return and active risk triple proportionately, so the ratio stays the same. The IR of an unconstrained portfolio is unaffected by the aggressiveness of the active weights.

What happens to the information ratio when you combine an actively managed portfolio with an allocation to the benchmark portfolio?

The blended portfolio has the same information ratio as the original active portfolio — increasing the benchmark weight decreases active return and active risk proportionately, leaving the IR unchanged.

What is the information coefficient (IC), and how does it differ from the ex-post information coefficient (ICR)?

IC is the ex-ante (expected), risk-weighted correlation between active returns and forecasted active returns — a measure of manager skill. ICR is the ex-post version, measuring the actual correlation between active returns and expected active returns.

What is the transfer coefficient (TC), and when does TC = 1?

TC is the correlation between actual active weights and optimal active weights (optimal weight is positively related to expected active return and negatively related to expected active risk). For an unconstrained portfolio, actual weights equal optimal weights, so TC = 1. For a constrained portfolio (e.g., short-sale or active-risk constraints), TC may be less than 1. Formula: TC = CORR(μi/σi, Δwiσi).

What is breadth (BR)?

The number of independent active bets taken per year. Example: a manager taking active positions in 10 securities each month has BR = 10 × 12 = 120.

authorized participants (APs)

APs are large broker-dealers that make the market in that ETF as primary market participants. APs are permitted to create additional shares, or redeem existing shares, for a service fee payable to the ETF manager. This creation/redemption process is in-kind: APs deliver a basket of securities (which may include cash) to the issuer in exchange for a number of ETF shares.

The in-kind creation/redemption process serves three purposes

1. Lower cost: The creation/redemption process does not force the ETF manager to sell/purchase portfolio investments; the manager does not incur any resulting transaction cost. The ETF manager usually collects a service charge from the AP to cover any incidentals.

2. Tax efficiency: A major benefit of the in-kind creation/redemption process is that it is not a taxable event. For a mutual fund, liquidity needs for redemption are often met by the fund manager by selling some of the fund's holdings, which triggers transaction costs as well as potential capital gains taxes. These costs are borne by all the shareholders of the fund (including those that did not redeem shares). Additionally, ETF managers can choose to publish customized redemption baskets, allowing them to target low-basis stocks that will be part of the redemption basket. This increases the tax efficiency (i.e., increases the basis) of the remaining holdings of the ETF.

3. Keeping market prices in line with NAV: APs will engage in arbitrage transactions if the ETFs trade at a price significantly different from their NAV. If the ETF trades at a premium, APs can sell the ETF, purchase the creation basket, and recreate those shares. Similarly, if the ETF trades at a significant discount to NAV, the APs can purchase the ETF and redeem the shares.

Sources of tracking error

1. Fees and expense. Fees reduce a fund's return.

2. Sampling and optimization. ETFs may use statistical techniques to replicate the performance of a benchmark without investing in all the securities that the index covers. Optimization techniques often favor higher-liquidity securities (and larger market cap companies) to minimize transaction cost. As a result, the ETF may impart a size bias relative to the benchmark.

3. Depository receipts (DRs). Foreign index ETFs often invest in DRs (rather than less-liquid securities traded on local exchanges). Any difference between the price of DRs and corresponding security (e.g., due to time zone differences in capturing price data) may contribute to tracking error of the ETF. Furthermore, sometimes an ETF may invest in other (sector) ETFs, and thus inherit the tracking errors of those ETFs.

4. Index changes. Index providers will occasionally rebalance or reorganize their indexes. ETF managers often use the creation/redemption process to rebalance the ETF portfolio to reflect this change in the index. The resulting delays from the use of the creation/redemption process contributes to tracking error. Because changes to an index are relatively infrequent, this component is often the smallest contributor to total tracking error.

5. Regulatory and tax requirements. In some countries, tax rates for foreign investors and domestic investors differ, leading to a difference in after-tax returns between an ETF and the index that it tracks.

6. Fund accounting practices. The time of the day when ETF NAV is calculated versus when the index provider performs this computation can lead to differences in calculated returns. Additionally, ETFs with foreign-currency-denominated holdings may use exchange rate values captured at a different time than the rate used by the index provider.

7. Asset manager operations. ETF managers may try to lower their cost by lending their shares to short sellers, and by foreign dividend capture (i.e., by working with foreign governments to minimize the taxes on distributions received). These methods tend to improve ETF performance relative to their benchmark.

The authorized participants (APs) in an ETF are most likely to be required to settle their ETF trades in

6 days