understand the concept of return‚ and be able to distinguish between realised returns and expected returns ● understand the relationship between expected return and risk ● understand the basic notion of uncertainty and be able to calculate sample variance ● understand the role and importance of the normal distribution. Key points 1 Investing involves allocating wealth to yield future returns. 2 Investments are typically measured according to risk and return. 3 The investment process can be broadly
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STA304 H1 S/1003 H S Winter 2013 Dragan Banjevic (I) Note: A lot of material will be used from Internet‚ some with reference‚ some without. 2 CITY OF TORONTO NEIGHBOURHOODS 1 West Humber-Clairville 19 Long Branch 36 Newtonbrook West 54 O’Connor-Parkview 2 Mount Olive-SilverstoneJamestown 20 Alderwood 37 Willowdale West 55 Thorncliffe Park 3 Thistletown-Beaumond Heights 21 Humber Summit 38 Lansing-Westgate 56 Leaside-Bennington 4 Rexdale-Kipling
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Module 2 2-2 Case Study: Helping the Moores Moore Housing Contractors QSO600: Operations Management Irfan Sheikh Moore Housing Contractors CPM/PERT network for Moore House Contractors Activity Activity Activity Duration Variance ES LS EF LF Slack a 4.167 .25 0 0.000 4.167 4.167 C r i t i c a l b 3.167 .25 4.167 4.167 7.333 7.333 C r i t i c a l c 3.833 .25 7.333 7.833 11.167 11.667 .500 d 2.167 .25 7.333 33.833 36 36 26.5 e 2 .111 7.333 7.333 9.333 9.333 C r i t i c a l Dumck
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sample obtained from the preschool delay task of Gordon Diagnostic System (Gordon‚ 1983). However‚ does higher dosage lead to higher cognitive performance? Histogram: Box-and-whisker plot: Multi plot: Summary statistics: Column n Mean Variance Std. dev. Std. err. Median Range Min Max Q1 Q3 Placebo 24 39.75 128.02174 11.314669 2.3095972 36 45 26 71 33 47 0.60 24 44.708333 151.7808 12.319935 2.5147962 42.5 48 29 77 35 54 Simple linear regression results: Dependent Variable: .60 mg/kg
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stocks. b. Calculate the variance and standard deviation of the small company returns and large company common returns. 5. The table below provides a probability distribution for the returns on stocks A and B State Probability Return On Stock A Return OnStock B 1 20% 5% 50% 2 30% 10% 30% 3 30% 15% 10% 4 20% 20% -10% a. Given a probability distribution of returns‚ calculate the expected return‚ variance‚ standard deviation of Stock
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Assignment for Week -2 Chapter 5 (5 - 9) Bond Valuation and Interest Rate Risk Bond L Bond S INS = $100 INS = $100 M = $1‚000 M = $1‚000 N = 15 Years N = 1 Year a) 1) rd = 5% VBL = INT/ (1 + rd)t + M/ (1 + rd)N =INT [1/rd – 1/ rd(1 + rd)N ] + M/ (1 + rd)N =$100 [1/0.05 – 1/ 0.05(1 + 0.05)15] + $1‚000/ (1 + 0.05)15 =$1040 + $480.77 = $1518.98
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09 Expected value = E(x) = ∑ x*P (x) = 1.03 Variance = E(x2) – [E(x)]2 = 1.09-1.03*1.03 = 0.0291 c. y 1 2 3 4 5 Total P(y) 0.96463 0.03330 0.00149 0.00009 0.00002 1.00 d. y 1 2 3 4 5 Total P(y) 0.96463 0.03330 0.00149 0.00009 0.00002 1.00 y*P (y) 0.96463 0.06660 0.00446 0.00034 0.00008 1.04 y2*P (y) 0.96463 0.13319 0.01337 0.00138 0.00041 1.11 Expected value = E(x) = ∑ x*P (x) = 1.04 Variance = E(x2) – [E(x)]2 = 1.11-1.04*1.04 = 0.0284 e
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A population of measurements is approximately normally distributed with mean of 25 and a variance of 9. Find the probability that a measurement selected at random will be between 19 and 31. Solution: The values 19 and 31 must be transformed into the corresponding z values and then the area between the two z values found. Using the transformation formula from X to z (where µ = 25 and σ √9 = 3)‚ we have z19 = (19 – 25) / 3 = -2 and z31 = (31 - 25) / 3 = +2 From the area between z =±2 is 2(0
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Problems on Risk and Return 1) Using the following returns‚ calculate the arithmetic average returns‚ the variances and the standard deviations for X and Y. Year X Y 1 8% 16% 2 21 38 3 17 14 4 -16 -21 5 9 26 2) You bought one of the Great White Shark Repellant Co’s 8 per cent coupon bonds one year ago for $1030. These bonds make annual payments and mature six years from now. Suppose you decide to sell your bonds today ‚when the required return on the bonds is 7 per cent
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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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