Lecture 9

Mutual Funds and

Performance Measurement

Unit Investment Trusts

Unit trusts are pools of money invested in a fixed portfolio (unmanaged) for the life of the fund.

All income and principals are paid out to the shareholders.

It is not traded on the market. Investors may sell shares back to the trustee for the net asset value. The trustee needs to liquidate some assets or finds a new investor.

Open-end Funds

Two types of managed investment companies: Open-end funds and close-end funds.

Investors can buy or sell shares in open-end funds at any time back to the fund. It is similar to bank demand deposit in this regard.

Fees: load vs. no load; front-end or back-end load; other fees.

The number of mutual funds in the US has exceeded the number of stocks. At the end of 2001, there were 7177 listed stocks in the US (based

on CRSP data) and 8307 mutual funds (2002 Mutual Fund Fact Book).

Close-end Funds

Close-end funds do not redeem or issue shares. Investors can trade the shares in the open market.

Close-end fund puzzle: market prices of closed-end funds are often different from their net asset values (NAVs). A large percentage of them are traded at a discount.

The NAV is the market value of the fund’s net asset values per share.

Real Estate Investment Trusts (REITs)

REITs invest in real estate or loans secured by real estate. They are closed-end funds. They are called property trusts in Australia.

Besides issuing shares, they raise capital by borrowing from banks and issue bonds or mortgages, so they are highly leveraged.

Two types: equity trusts invest in real estate directly; mortgage trusts invest primarily in mortgage and construction loans.

Investing in Real Estate: Direct holding or buying REITs?

Investment Policies

Two broad categories: passively or actively managed funds. Index funds are passively managed funds.

There are many types of actively managed funds, depending on objectives. But many of them are “closet indexers.”

Investment policies: maximum capital gains, stable income, sector, emerging markets, fixed-income, etc. However, investment style of a fund may be different from its policy.

Index Funds

Funds hold shares in proportion to their representation in certain stock market index.

“Tracking error” problem: too many stocks are included in the index. It is

uneconomical to trade in every security included in the index.

Transaction costs prevent the fund from closely track the index.

Exchange-Traded Funds (ETF)

An exchange-traded fund as a mutual fund that trades like a stock. Just like an index fund, an ETF represents a basket of stocks that reflect an index.

It has fancy names such as: Spiders: because of their SPDR ticker symbol. It is the first ETF

(started in 1993) based on S&P 500; Diamonds: the ticker symbol is DIA. It tracks the Dow-Jones

Industrial Average; Cubes: ticker symbol QQQQ, tracking NASDAQ index; ETFs reached Australia in March 2001 when Salomon Smith

Barney launched its Index Shares 100 product (ASX code IDX). In August 2001, State Street Global joined the fray with the Street Tracks 200 and Street Tracks 50 (ASX codes STW and SFY).

Hedge Funds

“Hedge funds” do not hedge. They seek arbitrage opportunities in the market.

Characteristics: flexible investment strategies, strong managerial incentives, substantial managerial investment, sophisticated investors, limited government oversight.

Who are Good Funds Managers?

Chevalier and Ellison (1999) found that young managers do better. A manager who is 1 year

older than another is expected to achieve a 8.6 basis points lower return.

Managers with MBAs outperform those without MBAs by 63 basis points.

Managers who graduated from higher-SAT schools obtain higher returns.

Calculating the Returns

Dollar-weighted Returns: using the discounted cash flow approach to find the IRR of your investment.

Time-weighted Returns: the average of the time period you hold the investment. arithmetic returns geometric returns which one is better? It depends.

Example

You bought a share at $50 at t=0, and another share at $53 at t=1. You sell the shares at $54 per share at t=2. The dividend is $2 per year.

What is the average returns of your investment? dollar-weighted average: 7.117% arithmetic average: 7.83% geometric average: 7.81% Note: geometric mean < arithmetic mean.

Sharpe Ratio

Sharpe Ratio:

It is the reward-to-variability ratio. It is not appropriate for non-diversified portfolios.

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Treynor’s Measure

It measures excess return per unit of systematic risk.

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Jensen’s Measure

It is the portfolio’s alpha value: the average return on the portfolio over and above that predicted by the CAPM, given the portfolio’s beta.

How to use Multi-factor models to calculate alphas?

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Appraisal Ratio (Information Ratio)

It adjusts the alpha of the portfolio by the nonsystematic risk. It measures abnormal return per unit of risk that in principle could be diversified away. It is equal to

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Using a Benchmark

It is common for the money manager and the plan sponsor to agree in advance on a benchmark to be used for judging performance.

Then the performance of the fund is judged by the difference in returns of this fund and the benchmark portfolio.

Benchmark Definitions

Equal-weighted portfolio: Assumes that equal proportions of wealth are invested in each asset.

Value-weighted portfolio: Assumes that market value proportions are reflected in the portfolio.

Price-weighted portfolio: Assumes that equal numbers of shares are invested in each asset.

How often to rebalance the portfolio? Need to consider transaction costs.

How Easy to Beat the Benchmark

Not easy because of transaction costs: the closing price may be different from the actual

executed price; benchmark portfolios do not consider brokerage fees,

etc. But the benchmark might also understate realistic

performance. For example, quoted benchmarks often do not include dividend income.

“Market Neutral” Strategy

Market neutral strategy: construct a portfolio by longing certain stocks and shorting others to make the portfolio’s beta at the level of zero.

What is the performance benchmark of such a market neutral strategy? --- T-bill rates?

What if lots of small stocks are held in such a portfolio?

Absolute return funds use market neutral strategy.

Market Timing

Market timing involves shifting funds between stocks and safe government securities such as T-bills.

A fund’s manager who has market timing ability should shift into more stocks in the bull market, and invest more in T-bills in the bear market.

Such market timing ability could produce a nonlinear convex relationship between the portfolio’s excess return and the market excess return.

Example of Market Timing

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Steadily Increasing the Beta

Empirical Testing

Treynor and Mazuy,

Hypothesis: c > 0. Little evidence of timing ability. Henriksson and Merton, (D is a Dummy variable)

Hypothesis: c > 0. Again, little evidence overall. 62% had negative c.

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Jensen’s Measure Revisited

“Jensen’s measure” can be explained as the average return on the active portfolio being evaluated against the average return on a passive benchmark portfolio with the same beta.

For example, if the beta of the active portfolio is 0.6, then the passive benchmark portfolio combines the market (e.g., All Ords) and cash (90-day Bank Bills rate) with 60-40 weights.

A positive means a good performance against the benchmark.

Jensen’s Measure in a Multi-factor Model

Jensen’s measure can be extended to multi-factor models. Assume that returns on all assets are generated by a two-factor model,

rit = E(rit) + bi1 F1t + bi2 F2t +eit

The following factor sensitivities are given for portfolio “ACTIVE” as well as two passive portfolios, the market index (“S&P/ASX 200) and a small-stock index (“SMALL”).

Portfolio bi1 bi2

ACTIVE 0.5 0.5 S&P/ASX 200 1.0 0.5 SMALL 0.5 1.0

Constructing a Benchmark

The benchmark portfolio must match the sensitivities of ACTIVE to each factor.

Let x, y, and z denote the benchmark portfolio’s weights in the S&P/ASX 200, SMALL, and cash.

Matching the betas, as well as having the portfolio weights sum to 1, requires

0.5 = 1.0 x + 0.5 y 0.5 = 0.5 x + 1.0 y 1 = x + y + z This gives x = y = z = 1/3.

Risk Adjusted Performance Assume that average returns are given below. Average Return ACTIVE 10% S&P/ASX 200 8% SMALL 12% Cash 6% The average return for this equal-weighted benchmark

portfolio is: 1/3(.08 + .12 + .06) = .0866. The average return on ACTIVE minus the benchmark

average gives the risk-adjusted performance (alpha) 0.0134 (= 0.10 – 0.0866).

If you ignore the “size” premium, then the traditional Jensen’s measure is: 0.10 – [6% + 0.5*(0.08-0.06)] = 3%.

Please note the correction in the calculation here!