P1.T4.807. Classical value at risk (VaR) (Dowd Ch.2)

Discussion in 'Today's Daily Questions' started by Nicole Seaman, May 21, 2018.

  1. Nicole Seaman

    Nicole Seaman Administrator Staff Member Subscriber

    Learning objectives: Describe the mean-variance framework and the efficient frontier. Explain the limitations of the mean-variance framework with respect to assumptions about return distributions.


    807.1. Displayed below is a plot of the Capital Market Line (CML) according to the mean-variance framework. There are only two risky assets:
    • Risky Asset A has an expected return and volatility of 8.0%
    • Risky Asset B has an expected return and volatility of 20.0%


    Please note the graph also contains an Orange Circle and a Green Triangle. About this situation, each of the following is true EXCEPT which is false?

    a. If the risk-free rate is constant at 3.0%, then the slope of the CML is invariant to the correlation between A & B returns
    b. An investor can achieve an expected return greater than 20.0%, which is the expected return of Risky Asset B, if she is willing to borrow at the risk-free rate
    c. The Green Triangle represents the Market Portfolio: it is entirely allocated between Risky Assets A & B but without any allocation to the risk-free asset
    d. The Orange Circle represents the Minimum Variance portfolio: it generates a Sharpe ratio that in inferior to (less than) the Sharpe ratio of any position on the CML

    807.2. Dowd explains that daily financial data can be expressed in either loss(+)/profit(-) format, or profit(+)/loss(-) format. For example, in profit(+)/loss(-) format which is more natural to the actual math, a asset's expected gain is represented by a positive value while it's loss is represented by a negative. However, in risk it is also convenient to use loss(+)/profit(-) format such that losses are expressed by positive values.

    Assume our chosen format is loss(+)/profit(-), which is also just called "L/P." Our position's profits are normally distributed and given by the following two parameters:
    • The drift, µ, is equal to -$15.0 per annum, and
    • The volatility, σ is equal to $35.0 per annum.
    If the daily returns are i.i.d. with 250 trading days per year, which is nearest to the 20-day 95.0% confident absolute value at risk (aVaR)?

    a. -9.35
    b. 15.08
    c. 21.83
    d. 42.57

    807.3. Rebecca has determined that her equity portfolio's 25-day 95.0% confident absolute value at risk (aVaR) is given by -µ*Δt + σ*α*sqrt(Δt) = -12,000 + 208,000 = $196,000. She subsequently decides that she wants to translate this into a 10-day 99.0% confident aVaR. If the returns are i.i.d. and normally distributed, which of the following is nearest to the translated VaR?

    a. 133,300
    b. 150,000
    c. 180,530
    d. 195,400

    Answers here:
  2. SP_SK

    SP_SK New Member Subscriber

    Hi Nicole, I had a query on the question posted above, would these questions be included in the quiz set for the related topic in the study planner, or do I need to keep a track of all these daily questions separately for practice. It would be great if you can help guide the best way to navigate this, I am looking to appear for November 2018 Part 1 exam.

  3. Nicole Seaman

    Nicole Seaman Administrator Staff Member Subscriber

    Hello @SP_SK

    You do not need to keep track of these daily. Once we have a full set of questions for a reading, these will be compiled into a practice question set and published in the study planner under the appropriate reading. We have taken a small break from posting daily practice questions, but we will resume shortly.

    Thank you,

    • Agree Agree x 1

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