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LOS m: Explain the sources of active risk, define and interpret tracking error, tracking risk, and the information ratio, and explain factor portfolio and tracking portfolio

A portfolio with a factor sensitivity of one to a particular factor in a multi-factor model and zero to all other factors is called a(n):

A factor portfolio is a portfolio with a factor sensitivity of one to a particular factor and zero to all other factors. An arbitrage portfolio is a portfolio with factor sensitivities of zero to all factors, positive expected net cash flow, and an initial investment of zero. A tracking portfolio is a portfolio with a specific set of factor sensitivities designed to replicate the factor exposures of a benchmark index.

A portfolio manager uses a two-factor model to manage her portfolio. The two factors are confidence risk and time-horizon risk. If she wants to bet on an unexpected increase in the confidence risk factor (which has a positive risk premium), but hedge away her exposure to time-horizon risk (which has a negative risk premium), she should create a portfolio with a sensitivity of:

A)	1.0 to the confidence risk factor and -1.0 to the time-horizon factor.

B)	?1.0 to the confidence risk factor and 1.0 to the time-horizon factor.

C)	1.0 to the confidence risk factor and 0.0 to the time-horizon factor.

She wants to create a confidence risk factor portfolio, which has a sensitivity of 1.0 to the confidence risk factor and 0.0 to the time horizon factor. Because the risk premium on the confidence risk factor is positive, an unexpected increase in this factor will increase the returns on her portfolio. The exposure to the time-horizon risk factor has been hedged away, because the sensitivity to that factor is zero.

Janice Barefoot, CFA, has been managing a portfolio for a client who has asked Barefoot to use the Dow Jones Industrial Average (DJIA) as a benchmark. In her second year, Barefoot used 29 of the 30 DJIA stocks. She selected a non-DJIA stock in the same industry as the omitted DJIA stock to replace that stock. Compared to the DJIA, Barefoot placed a lower weight on the communication stocks and a higher weight on the other stocks still in the portfolio. Over that year, the non-DJIA stock in the portfolio had a positive and higher return than the omitted DJIA stock. The communication stocks had a negative return while all of the other stocks had a positive return. The portfolio managed by Barefoot outperformed the DJIA. Based on this we can say that the return from factor tilts and asset selection were:

A)	negative and positive respectively.

B)	both positive.

C)	positive and negative respectively.

Since the communications stocks had a negative return while all the other stocks had a positive return, Barefoot’s underweighting of those stocks produced a positive tilt return. Since the asset chosen to replace the DJIA stock outperformed the omitted stock, the asset selection return was positive.

A common strategy in bond portfolio management is enhanced indexing by matching primary risk factors. This strategy could be implemented by forming:

A)	a portfolio with factor sensitivities that sum to one.

B)	a portfolio with asset portfolio weights equal to that of the index.

C)	a portfolio with factor sensitivities equal to that of the index.

Enhanced indexing by matching primary risk factors could be implemented by creating a tracking portfolio with the same factor sensitivities as the index but with a different set of bonds. Then any differences in performance between the portfolio and the benchmark index will be the result of bond selection ability and not from different exposures to macroeconomic factors like GDP, inflation, and interest rates.

A portfolio with a specific set of factor sensitivities designed to replicate the factor exposures of a benchmark index is called a:

A tracking portfolio is a portfolio with a specific set of factor sensitivities designed to replicate the factor exposures of a benchmark index. A factor portfolio is a portfolio with a factor sensitivity of one to a particular factor and zero to all other factors. An arbitrage portfolio is a portfolio with factor sensitivities of zero to all factors, positive expected net cash flow, and an initial investment of zero.

Janice Barefoot, CFA, has been managing a portfolio for a client who has asked Barefoot to use the Dow Jones Industrial Average (DJIA) as a benchmark. In her first year Barefoot managed the portfolio by choosing 29 of the 30 DJIA stocks. She selected a non-DJIA stock in the same industry as the omitted stock to replace that stock. Compared to the DJIA, Barefoot has placed a higher weight on the financial stocks and a lower weight on the other stocks still in the portfolio. Over that year, the non-DJIA stock in the portfolio had a negative return while the omitted DJIA stock had a positive return. The portfolio managed by Barefoot outperformed the DJIA. Based on this we can say that the return from factor tilts and asset selection were:

A)	negative and positive respectively.

B)	both positive.

C)	positive and negative respectively.

Since the replacement of the asset obviously had a negative effect, the tilting towards financial stocks must have been positive to not only compensate for the loss but produce a portfolio return greater than the DJIA.

Janice Barefoot, CFA, has managed a portfolio where she used the Dow Jones Industrial Average (DJIA) as a benchmark. In the past two years the average monthly return on her portfolio has been higher than that of the DJIA. To get a measure of active return per unit of active risk Barefoot should compute the:

A)	information ratio, which is the standard deviation of the differences between the portfolio and benchmark returns divided into the average of those differences.

B)	information ratio, which is the standard deviation of the differences between the portfolio and benchmark returns divided by the average of those differences.

C)	Sharpe ratio, which is the standard deviation of the differences between the portfolio and benchmark returns divided into the average of those differences.

The information ratio is the measure of active return per unit of active risk. If we let X = (monthly portfolio return ? the benchmark return), then the information ratio = (the average of X / the standard deviation of X). It is similar to the Sharpe ratio, which defines the random variable Y as Y = (monthly portfolio return ? the risk-free rate). The Sharpe ratio = (the average of Y / the standard deviation of the portfolio return) = the standard deviation of Y if the risk-free rate is constant.

A)	factor sensitivities of zero to all factors, positive expected net cash flow, and an initial investment of zero.

B)	a factor sensitivity of one to a particular factor in a multi-factor model and zero to all other factors.

C)	a specific set of factor sensitivities designed to replicate the factor exposures of a benchmark index.

A)	a specific set of factor sensitivities designed to replicate the factor exposures of a benchmark index.

B)	factor sensitivities of zero to all factors, positive expected net cash flow, and an initial investment of zero.

C)	a factor sensitivity of one to a particular factor in a multi-factor model and zero to all other factors.

Sidney Peterson is starting a new fund that is designed to have the same factor exposures as the Dow Jones Industrial Average, but seeks to outperform the index by at least 2% annually thorough superior stock selection. To achieve this, the fund would most likely use a:

Tracking portfolios are typically used for active asset selection. A pure factor portfolio would be used to increase or decrease exposure to one specific factor, such as GNP. A bottom-up strategy is unsuitable because it solely focuses on a firm’s characteristics and fails to properly invest in the same industries as the index.

The Real Value Fund is designed to have zero exposure to inflation. However its current inflation factor sensitivity is 0.30. To correct for this, the portfolio manager should take a:

A)	30% short position in the inflation factor portfolio.

B)	30% short position in the inflation tracking portfolio.

C)	30% long position in the inflation factor portfolio.

To hedge inflation, the fund should take a 30% short position in the inflation factor portfolio. This short position will fully offset the fund’s positive exposure to inflation. Tracking portfolios are typically used for active asset selection and have multiple factor exposures which would prevent them from adequately hedging the inflation exposure of the fund.

An analyst is constructing a portfolio for a new client. A portfolio which uses multifactor models to create a portfolio with an exposure to only one type of risk is:

A factor portfolio is established to create exposure to a specific risk (i.e. inflation).

An analyst is constructing a portfolio for a new client. A portfolio which has factor exposures matched to those of a benchmark is:

A)	an arbitrage portfolio.

B)	a tracking portfolio.

C)	an efficient portfolio.

A tracking portfolio has factor exposures matched to those of a benchmark.