FINM2003 Study Guide - Final Guide: Tracking Error, Standard Deviation, Systematic Risk

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30 Jun 2018

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Portfolio Performance Evaluation

- Tools to evaluate the performance of a given portfolio , how we can measure the

return of a portfolio and to adjust the return measures to account for the risk of the

portfolio

Measuring the return on an investment

1. Measure r as the following

2. Discounted Cash Flow Approach to get the same result , this derives internal rate of

return or dollar-weighted rate of return

3. Time-weighted return(also arithmetic average of returns in each period)-

considers the returns earned on the asset in each period, but ignores the actual amount

investment in the asset in each period

4. Geometric average return

r can be considered as the HPR

More generally

*Geometric averages will always be less than arithmetic averages

Arithmetic v Geometric

1. If looking at historical investment performance: geometric averages measure the

constant rate of return an investment would have needed to provide in each period to

generate the final value of the investment

2. If looking at future performance: geometric provides a downward biased estimate of

future performance, so it would be preferable to use arithmetic averages

But historical returns are often used to create expectations regarding future returns, so

estimates are subject to sampling error

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Document Summary

Tools to evaluate the performance of a given portfolio , how we can measure the return of a portfolio and to adjust the return measures to account for the risk of the portfolio. *geometric averages will always be less than arithmetic averages. If looking at historical investment performance: geometric averages measure the constant rate of return an investment would have needed to provide in each period to generate the final value of the investment. If looking at future performance: geometric provides a downward biased estimate of future performance, so it would be preferable to use arithmetic averages. Where h/t is , investment horizon/historical sample period t. Returns must be risk-adjusted for meaningful comparisons: sharpe"s measure : excess return per unit of total risk. Given same risk, comparison will allow meaningful conclusions. Assume that portfolio p has a standard deviation of 42%, and the market exhibits a standard deviation of 30%.

Related Questions

1. Which of the following statements about defined contribution plans is incorrect?

a. In general, employees can choose the investment vehicle under a defined contribution plan. Thus, highly risk-averse employees can choose low-risk investments, while more risk-tolerant employees can choose high-risk investments.

b. In a defined contribution plan, the employer must make larger-than-average contributions to the pension plan when investment returns have been below expectations.

c. Defined benefit plans are used more often by large corporations than by small companies.

d. The PBGC insures a portion of pension benefits.

e. A defined contribution plan places the risk of poor pension portfolio performance on the employee.

2. Which of the following statements about pension plan portfolio performance is incorrect?

a. Alpha analysis, which relies on the Capital Asset Pricing Model, considers the risk of the portfolio when measuring performance.

b. Peer comparison examines the relative performance of portfolio managers with similar investment objectives.

c. A portfolio annual return of 12 percent from one investment advisor is not necessarily better than a return of 10 percent from another advisor.

d. In managing the retiree portfolio, fund managers often use immunization techniques such as alpha analysis to eliminate, or at least significantly reduce, the risk associated with changing interest rates.

e. Pension fund sponsors must evaluate the performance of their portfolio managers periodically as a basis for future asset allocations.

3. Ms. Lloyd, who is 25 and expects to retire at age 60, has just been hired by the Chambers Corporation. Ms. Lloyd's current salary is $30,000 per year, but her wages are expected to increase by 5 percent annually over the next 35 years. Chambers has a defined benefit pension plan in which workers receive 2 percent of their final year's wages for each year of employment. Assume a world of certainty. Further, assume that all payments occur at year-end. What is Ms. Lloyd's expected annual retirement benefit, rounded to the nearest thousands of dollars?

a. $35,000

b. $57,000

c. $89,000

d. $116,000

e. $132,000

blackdolphin35

Mary and Nick Stalcheck have an investment portfolio containing four vehicles. It was developed to provide them with a balance between current income and capital appreciation. Rather than acquire mutual fund shares or diversify within a given class of investment vehicle, they developed their portfolio with the idea of diversifying across various types of vehicles. The portfolio currently contains common stock, industrial bonds, mutual fund shares, and options. They acquired each of these vehicles during the past three years, and they plan to invest in other vehicles sometime in the future.

Currently, the Stalchecks are interested in measuring the return on their investment and assessing how well they have done relative to the market. They hope that the return earned over the past calendar year in in excess of what they would have earned by investing in a portfolio consisting of the S&P 500 Stock Composite Index. Their research has indicated that the risk-free rate was 7.2% and that the (before-tax) return on the S&P 500 portfolio was 10.1% during the past year. With the aid of a friend, they have been able to estimate the beta of their portfolio, which was 1.20. In their analysis, they have planned to ignore taxes, because they feel their earnings have been adequately sheltered. Because a they did not make any portfolio transactions during the past year, all of the Stalchechk's investments have been held more than 12 months, and they would have to consider only unrealized capital gains, if any. To make the necessary calculations, the Stalchecks have gathered the following information on each of the four vehicles I their portfolio.

Common stock: They own 400 shares of KJ Enterprises common stock. KJ is a diversified manufacturer of metal pipe and is know for its unbroken stream of dividends. Over the past few years, it has entered now markets and, as a result, has offered moderate capital appreciation potential. Its share price has risen from $17.25 at the start of the last calendar year to $18.75 at the end of the year. During the year, quarterly cash dividends of $.20, $.20, $.25, and $.25 were paid.
Industrial bonds: The Stalchecks own eight Cal Industries bonds. The bonds have a $1,000 par value, have a 9.250% coupon, and are due in 2021. They are A-rated by Moody's. The bond was quoted at 97.000 at the beginning of the year and ended the calendar year at 96.375%.

Mutual funds: The Stalcheks hold 500 shares of Holt Fund, a balanced, no-load mutual fund. The dividend distributions on the fund during the year consisted of $.60 in investment income and $.50 in capital gains. The fund's NAV at the beginning of the calendar year was $19.45, and it ended the year at $20.02.

Options: The Stalchecks own 100 options contracts on the stock of a company they follow. The value of these contracts totaled $26,000 at the beginning of the calendar year. At year-end the total value of theoptions contracts was $29,000.

a. Calculate the holding period return on a before-tax basis for each of these four investment vehicles.

b) Assuming their ordinary income is currently being taxed at a combined tax rate of 38%. And that they would pay a 15% capital gains tax on dividends and capital gains for holding periods longer than 12 months, determine the after tax HPR for each of their 4 investment vehicles.

c) Recognizing that all gains on their investments were unrealized, calculate the before tax portfolio HPR for their 4 vehicle portfolio during the past calendar year. Evaluate this return relative to its current income and capital gain components.

d) Use the HPR calculated in question c to compute the Jensen's measure (Jensen alpha). Use that measure to analyze the performance of their portfolio on a risk adjusted, market adjusted basis. Comment on your finding. Is it reasonable to use Jensen's measure to evaluate a 4 vehicle portfolio? Why or why not?

Kelli Blakely is a portfolio manager for the Miranda Fund (Miranda), a core large-cap equity fund. The market proxy and benchmark for performance measurement purposes is the S&P 500. Although the Miranda portfolio generally mirrors the asset class and sector weightings of the S&P, Blakely is allowed a significant amount of leeway in managing the fund. Her portfolio holds only stocks found in the S&P 500 and cash.

Blakely was able to produce exceptional returns last year (as outlined in the table below) through her market timing and security selection skills. At the outset of the year, she became extremely concerned that the combination of a weak economy and geopolitical uncertainties would negatively impact the market. Taking a bold step, she changed her market allocation. For the entire year her asset class exposures averaged 50% in stocks and 50% in cash. The S&Pâs allocation between stocks and cash during period was a constant 97% and 3%, respectively. The risk-free rate of return was 2%.

One-Year Trailing Returns

	Miranda Fund	S&P 500

Return	10.2%	â22.5%
Standard deviation	37%	44%
Beta	1.10	1.00

a.	What are the Sharpe ratios for the Miranda Fund and the S&P 500? (Do not round intermediate calculations. Enter answer values in decimals. Negative amount should be indicated by a minus sign. Round your answer to 4 decimal places.)

Sharpe ratio for the Miranda Fund
Sharpe ratio for the S&P 500

b.	What are the M ² measures for Miranda? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.)

M ² measure for Miranda

c.	What is the Treynor measure for the Miranda Fund and the S&P 500? (Do not round intermediate calculations. Enter answer values in decimals. Round your answer to 4decimal places.

Treynor measure for the Miranda Fund
Treynor measure for the S&P 500

d.	What is the Jensen measure for the Miranda Fund? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Jensen measure for the Miranda Fund

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FINM2003 Study Guide - Final Guide: Tracking Error, Standard Deviation, Systematic Risk

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