Investment Risk Management 2024-2025

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Questions and Answers

What does the breadth (BR) of a portfolio represent?

  • The average return of the securities
  • The number of securities in the portfolio (correct)
  • The total value of all securities in the portfolio
  • The risk level of the portfolio

Which formula represents the expected active return, E(RA)?

  • E(RA) = BR * σA * TC / IC
  • E(RA) = BR + TC + IC + σA
  • E(RA) = IC * BR / TC
  • E(RA) = TC * IC * BR * σA (correct)

What does the transfer coefficient (TC) indicate in the fundamental law of active management?

  • The volatility of active security weights
  • The potential for market return
  • The degree of active management effectiveness (correct)
  • The average risk of securities

Which of the following parameters is NOT involved in the full fundamental law formula for expected active return?

<p>Expected market return (C)</p> Signup and view all the answers

How is the information ratio (IR) related to active management?

<p>IR is the ratio of expected active return to portfolio active risk (C)</p> Signup and view all the answers

What is the formula for the return on a combined portfolio?

<p>$R_C = w_P R_P + (1 - w_P) R_F$ (B)</p> Signup and view all the answers

Which of the following statements about volatility of the combined portfolio is true?

<p>It is equal to $STD(R_C) = w_P STD(R_P)$. (A)</p> Signup and view all the answers

The Sharpe ratio for the combined portfolio is equivalent to the Sharpe ratio of which element?

<p>The risky asset portfolio (C)</p> Signup and view all the answers

What criterion is considered the best for assessing active performance among various managed funds?

<p>Expected information ratio (C)</p> Signup and view all the answers

According to the fundamental law of active management, what limits the active return in a managed portfolio?

<p>The limit on active risk (B)</p> Signup and view all the answers

What does the total risk of an actively managed portfolio consist of?

<p>The sum of benchmark return variance and active return variance (A)</p> Signup and view all the answers

Which mathematical expression correctly represents the relationship between the squared Sharpe ratio and the squared information ratio?

<p>$SR_P^2 = SR_B^2 + IR^2$ (C)</p> Signup and view all the answers

What represents the optimal risky asset portfolio according to mean-variance theory?

<p>The portfolio tangent to a ray extended from the risk-free rate (C)</p> Signup and view all the answers

What does the formula $R_A = R_P - R_B$ represent in active management?

<p>The active return of an actively managed portfolio (D)</p> Signup and view all the answers

If $∆w_i$ is negative, how is this assessed against the benchmark weight?

<p>It reflects an underweight position (D)</p> Signup and view all the answers

Which of the following is NOT a quality for a benchmark to serve as a relevant comparison in active management?

<p>Replicability at high cost (B)</p> Signup and view all the answers

In the context of value added, which of the following represents asset value added from security selection?

<p>$w_P,j R_{A,j}$ (D)</p> Signup and view all the answers

What is the Sharpe Ratio used to measure?

<p>Risk-adjusted performance of a portfolio (C)</p> Signup and view all the answers

What is the implication of adding cash or leverage to a portfolio with respect to the Sharpe Ratio?

<p>It has no effect on the Sharpe Ratio (D)</p> Signup and view all the answers

What does $R_A = ∑ ∆w_j R_{B,j} + ∑ w_P,j R_{A,j}$ specifically reflect?

<p>Value added from asset allocation and security selection (B)</p> Signup and view all the answers

Which mathematical relationship signifies an 'overweight' position compared to the benchmark weight?

<p>$∆w &gt; 0$ (B)</p> Signup and view all the answers

What component is included in the calculation of the standardized return formula for a portfolio?

<p>Risk-free rate (C)</p> Signup and view all the answers

What does the term $R_{A,i}$ represent in the context of active security returns?

<p>The active return of a security (C)</p> Signup and view all the answers

How can the active security return be calculated using a multi-factor statistical model?

<p>$R_{A,i} = R_i - ext{sum of factors}$ (D)</p> Signup and view all the answers

What does the transfer coefficient (TC) measure?

<p>The degree to which active weights translate to active returns (A)</p> Signup and view all the answers

What is the information coefficient (IC) based on?

<p>The correlation between forecasts and realized risk-weighted returns (D)</p> Signup and view all the answers

Which formula represents the expected active portfolio return?

<p>$E(R_A) = ext{sum product of active weights and forecasted returns}$ (C)</p> Signup and view all the answers

In the expression $TC = ext{COR}( rac{μ}{σ}; Δw_i) rac{σ_i}{σ}$, what does $μ$ represent?

<p>The forecasted active return (C)</p> Signup and view all the answers

The term $β_{j,i}$ in the multi-factor model represents what?

<p>The correlation between a security and a market factor (C)</p> Signup and view all the answers

Which of the following statements regarding active security returns is true?

<p>Active security returns can be negative. (D)</p> Signup and view all the answers

What does the symbol $ orall$ signify in the equation for the expected active return?

<p>The sum over all securities considered (D)</p> Signup and view all the answers

Which measure must be adjusted for risk to obtain the transfer coefficient?

<p>Active weights (B)</p> Signup and view all the answers

Flashcards

Active Return

The difference between the return on the actively managed portfolio and the return on the benchmark portfolio.

Sharpe Ratio

A measure of an investment's risk-adjusted return, calculated by dividing the excess return over the risk-free rate by the standard deviation of the investment's returns.

Benchmark Portfolio

A portfolio that represents the assets from which an investor will make their selections, typically consisting of passively managed assets.

Active Management

An investment strategy that involves actively selecting and trading securities to outperform a benchmark portfolio.

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Investment Risk Management

The process of minimizing the potential losses of an investment portfolio.

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Security Selection Value Added

The portion of the portfolio's return attributed to selecting securities that outperform the benchmark within each asset class.

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Asset Allocation Value Added

The portion of the portfolio's return attributed to allocating assets differently from the benchmark weights.

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Total Value Added

The sum of security selection value added and asset allocation value added.

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Active Weight

Overweighting or underweighting an asset class compared to the benchmark.

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Value Added Decomposition

The return on the actively managed portfolio is equal to the sum of the product of the active weights with the benchmark returns for each asset class plus the sum of the product of the portfolio weights with the active returns for each asset class.

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Information Ratio (IR)

The ratio of the excess return of an actively managed portfolio over its benchmark return to the standard deviation of the active return. It measures the performance of an active manager relative to their benchmark.

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Active Risk (StdDevRA)

The standard deviation of an actively managed portfolio's return relative to its benchmark. It measures the risk associated with an active manager's deviation from the benchmark.

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Optimal Risky Asset Portfolio

The optimal portfolio of risky assets that yields the highest Sharpe ratio. It's the point on the efficient frontier tangent to a ray extending from the risk-free rate.

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Sharpe Ratio of Risk-Free Asset

The ratio of the risk-free rate to the standard deviation of the risk-free rate return. Since the risk-free rate is constant, it doesn't vary and has a Sharpe ratio of 0.

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Sharpe Ratio of Portfolio (SR)

The ratio of the total return of a portfolio to the standard deviation of the total return. It measures the risk-adjusted return of the portfolio.

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Benchmark Tracking Risk

The standard deviation of the excess return of the managed portfolio over the benchmark. It measures the risk associated with active portfolio management.

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Fundamental Law of Active Management

A relationship that states that the square of the Sharpe ratio of a portfolio is equal to the sum of the square of the Sharpe ratio of the benchmark and the square of the Information Ratio. It shows the relationship between active management and overall portfolio performance.

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Total Risk (StdDevRP)

The variance of the return of a portfolio. It measures the total risk of the portfolio.

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Breadth (BR)

The number of securities in a portfolio.

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Transfer Coefficient (TC)

The ability of an active manager to translate their investment ideas into portfolio positions. It quantifies how effectively the manager can execute their investment decisions.

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Information Coefficient (IC)

The correlation between the manager's forecasts and actual security returns. It quantifies the manager's skill in predicting future returns.

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Active Return (RAi)

The difference between a security's return and the benchmark return.

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Expected Active Return (μi)

The investor's expected active return, representing their subjective expectation.

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Individual Security Active Return (RAi)

The residual return of a security after accounting for market-wide factor returns.

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Market-wide Factors (Rj)

Factors that influence market-wide returns, like market risk or interest rate changes.

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Security Sensitivities (βj,i)

The sensitivities of a particular security to market-wide factors.

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Expected Active Portfolio Return (E RA)

The anticipated value added for an actively managed portfolio, reflecting the expected return from active trading.

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Optimal Active Portfolio

The portfolio constructed using optimal security weights to maximize the expected active return.

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Fundamental Law of Active Portfolio Management

The fundamental relationship between expected active return, information coefficient, and active risk.

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Study Notes

Investment Risk Management 2024-2025

  • Course code: 6FNCE001C
  • Institution: Westminster International University in Tashkent
  • Course is about investment risk management specifically in the context of active portfolio management.

Active Portfolio Management

  • This module analyzes active portfolio management.
  • Active portfolio management focuses on generating value-added returns.
  • The course covers active management, risk and return, and the fundamental law of active management.

Active Management and Value Added

  • Measuring Value Added: Active return is the difference between portfolio and benchmark returns.
  • Active Return = Portfolio Return - Benchmark Return
  • RA = RP - RB
  • Value added formula: N RA= ∑ Awi Rai i=1
  • Awi is positive -> portfolio is overweight the benchmark
  • Awi is negative -> portfolio is underweight the benchmark

Comparing Risk and Return

  • Sharpe Ratio: A way to measure risk adjusted return
  • Sharpe Ratio = (Portfolio Return - Risk-Free Rate) / Portfolio Volatility
  • SR = (Rp - rf)/Std(R)

The Fundamental Law of Active Management

  • The active management's expected return is a key parameter that is made up of several factors.

  • The expected value added depends on factors like transfer coefficients, information coefficients, breadth, and active risk.

  • A critical concept is the concept of the transfer coefficient.

  • This represents the correlation between the forecasts of returns and the actual weights used in the investment portfolio.

  • The information coefficient is measured by the correlation between forecasts and realized returns, adjusted by risk.

  • The main idea expressed is: Expected active return = Transfer Coefficient * Information Coefficient * √Portfolio Breadth

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