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    9.understanding Risk

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    Ashesh Das

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    © All Rights Reserved
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    9.understanding Risk

    Uploaded by

    Ashesh Das
    44 views18 pages

    Original Title

    9.Understanding Risk

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    44 views18 pages

    9.understanding Risk

    Uploaded by

    Ashesh Das

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 18

    Understanding Risk

    McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
    Risk: Definition

    Risk is a measure of _________ about the


    future payoff of an investment,
    measured over some time horizon and
    relative to a benchmark.
    Measuring Risk

    1. List of all possible outcomes


    2. List the __________ of each occurring
    Measuring Risk
    Example: Single Coin Toss

    Lists all possibilities, one of them must occur.


    Probabilities sum to _______.
    Measuring Risk:
    Case 1
    Investing $1000

    Possibilities Probability Payoff

    1 0.5 $700

    2 0.5 $1400

    (Two possibilities are equally likely)


    Measuring Risk:
    Case 2
    Investing $1000

    Possibilities Probability Payoff


    1 0.1 $100
    2 0.4 $700
    3 0.4 $1,400
    4 0.1 $2,000
    Measuring Risk:
    Comparing Cases 1 & 2
    • What is the Expected value in both the cases?

    • Is the risk the same?


    Measuring Risk:
    Variance & Standard Deviation
    • Variance:
    Average of squared deviation of the
    outcomes from the expected value, weighted
    by the probabilities.

    • Standard Deviation:
    Square root of the variance
    (Same units as the payoff)
    Measuring Risk:
    Comparing Cases 1 & 2
    Case 1: Standard Deviation =$350
    Case 2: Standard Deviation =$528

    The greater the standard deviation, the


    ________ the risk.
    Leverage
    • Leverage:
    Borrowing to finance part of an investment
    Leverage _________ Expected return and risk.
    • Invest
    – $1000 or your own + $1000 borrowed
    – Expected return doubles
    – Standard Deviation doubles
    Risk-Return Tradeoff

    More risk  Bigger risk premium  Higher expected return

    Risk Requires Compensation


    Reducing Risk through Diversification
    Two ways to diversify your investments. You can

    1. hedge risks

    2. spread them among the many investments.


    Reducing Risk:
    Hedging
    Compare:
    1. Invest $100 in GE
    2. Invest $100 in Texaco
    3. Invest ½ in each:
    $50 in GE
    + $50 in Texaco
    Reducing Risk:
    Hedging
    Initial investment= $100

    Hedging has eliminated the risk entirely.


    Reducing Risk:
    Spreading
    • You can’t always hedge
    • The alternative is to spread risk around
    • Find investments whose payoffs
    are unrelated
    Reducing Risk:
    Spreading
    Consider three investment strategies:
    1. GE only,
    2. Microsoft only, and
    3. ½ in GE + ½ in Microsoft.
    Reducing Risk:
    Spreading

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