Investment Science Chapter 3 Dr. James A. Tzitzouris 3.1 Use A= 1− rP 1 (1+r)n with r = 7/12 = 0.58%‚ P = $25‚ 000‚ and n = 7 × 12 = 84‚ to obtain A = $377.32. 3.2 Observe that since the net present value of X is P ‚ the cash flow stream arrived at by cycling X is equivalent to one obtained by receiving payment of P every n + 1 periods (since k = 0‚ . . . ‚ n). Let d = 1/(1 + r). Then ∞ P∞ = P k=0 (dn+1 )k . Solving explicitly for the geometric series‚ we have that P∞ = Denoting
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exponential probability density function. If then the cumulative distribution function of the exponential distribution is The following is the plot of the exponential cumulative distribution function. Mean and variance of an exponential function The mean and variance of an exponential function are respectively Example 28 If jobs arrive every 15 seconds on average‚ λ= 4 per minute‚ what is the probability of waiting less than or equal to 30 seconds‚ i.e .5 min
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Covariance = 1/5 (-0.1-0.035)(0.21-0.04) + (0.2-0.035)(0.3-0.12) + (0.05-0.035)(0.07-0.12) + (-0.05-0.035)(-0.03-0.12) + (0.02-0.035)(-0.08-.012) + (0.09-0.035)(0.25-.012) = 0.00794 Variance of A = 1/5 (-0.1-0.035)2 + (0.2-0.08)2 + (0105 – 0.035)2 + (-0.05-0.035)2 + (0.02-0.035)2 + (0.09-0.035)2 = 0.01123 Variance of B = 1/5 (0.21-0.12)2 + (0.3-0.12)2 + (0.07-0.12)2 + (-0.03-0.12)2 (-0.08-0.12)2 + (0.25-0.12)2 = 0.02448 C. Correlation = 0.00794/(0.01123) (0.02448) = 0.479 12-4. Suppose all
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and an expected return of 3.5%‚ what kind of asset is it? Is it really risk-free? 5.Take the HMC management’s views of expected returns‚ standard deviation‚ and covariance of real returns as correct. Also‚ assume that cash is riskless (i.e. zero variance and covariance). If the board allows HMC to invest in only one asset class‚ which asset classes would you advise HMC to discard right away? Why? 6.If the board allows HMC to invest in assumed riskless cash and one other asset class‚ which asset
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that it produces is given by the function P(x) = 300 — 4x. The cost function is c(x) = 500 + 28x where x is the number of units produced. Find x so that the profit is maximum. Question: 1) Find the value of x. 2) In using regression analysis for making predictions what are the assumptions involved. 3) What is a simple linear regression model? 4) What is a scatter diagram method? CASE STUDY : 3 Mr Sehwag invests Rs 2000 every year with a company‚ which
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areas totaling 42% The Second will be the size chart. This will measure tendency‚ variation‚ mean‚ median and mode. Descriptive Statistics: Size Mean 3.42 Standard Error 0.24593014 Median 3 Mode 2 Standard Deviation 1.73898868 Sample Variance 3.02408163 Kurtosis -0.7228086 Skewness 0.52789598 Range 6 Minimum 1 Maximum 7 Sum 171 Count 50 Frequency Distribution: Size Frequency 1 5 2 15 3 8 4 9 5 5 6 5 7 3 The mean household size of the customers is given as 3.42
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EG40JQ/12 UNIVERSITY OF ABERDEEN SESSION 2011 – 2012 Degree Examination in EG40JQ SAFETY AND RELIABILITY ENGINEERING Friday 20 January 2012 Notes: (i) (ii) 2.00 p.m. – 5.00 p.m. Candidates ARE permitted to use an approved calculator Data sheets are attached to the paper. Candidates should attempt all FIVE questions. REGULATIONS: (i) You must not have in your possession any material other than that expressly permitted in the rules appropriate to this examination. Where
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| |COMPANY A | | | | | |BANK OF AMERICAN CO | |Date |Open |Close |Dividend |Return | |12/1/2005 |46 |46.15 |0.5 |0.014130435 | |11/1/2005 |43.75 |45.89 |0.5 |0.060342857 | |10/3/2005 |42.47 |43.74 |0.5 |0.041676478
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each question is independent of the others and assumptions from one question do not carry over to the others. 4. Use of a calculator is allowed. 5. Some useful equations are printed below. (a) Standard deviation: n (ri − r¯)2 i=1 σ(r) = n−1 (b) Variance of a portfolio: σ 2 = w12 σ12 + w22 σ22 + 2w1 w2 σ1 σ2 cov(R1 ‚ R2 ) = w12 σ12 + w22 σ22 + 2w1 w2 σ1 σ2 ρ1‚2 (c) Weighted average cost of capital: W ACC = ke × D E + kd (1 − t) × V V GOOD LUCK! Q UESTIONS 1 AND 2 (16 MARKS EACH ) 1. Inflation
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The value of an annuity of $RM1 per period for t years (t-year annuity factor) is: Measures of Risk: Variance of returns = σ2 = expected value of Standard deviation of returns‚ σ = Covariance between returns of stocks 1 & 2 = σ1‚2 = expected value of Correlation between returns of stocks 1 & 2: Beta of stock i = βi = The variance of returns on a portfolio with proportion xi invested in stock i is: A Growing Perpetuity (Gordon
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