Q1 The discount rate for the value of the option is the expected return on the stock: E(s) =r=0.02+3(0.1-0.02)=0.26 The call option has a positive value.

Slides:

Advertisements

Similar presentations

Question 1 (textbook p.312, Q2)

Advertisements

Quiz 4 solution sketches 11:00 Lecture, Version A Note for multiple-choice questions: Choose the closest answer.

AP Statistics Chapter 16. Discrete Random Variables A discrete random variable X has a countable number of possible values. The probability distribution.

FINANCE 8. Capital Markets and The Pricing of Risk Professor André Farber Solvay Business School Université Libre de Bruxelles Fall 2007.

Risk, Return, and Discount Rates Capital Market History The Risk/Return Relation Applications to Corporate Finance.

Covariance And portfolio variance Review question  Define the internal rate of return.

Combining Individual Securities Into Portfolios (Chapter 4)

Internal Rate of Return (IRR) and Net Present Value (NPV)

Complex Numbers Section 2.1. Objectives Rewrite the square root of a negative number as a complex number. Write the complex conjugate of a complex number.

Risk, Return, and Discount Rates Capital Market History The Risk/Return Relation Applications to Corporate Finance.

Théorie Financière Valeur actuelle Professeur André Farber.

Covariance And portfolio variance The states of nature model  Time zero is now.  Time one is the future.  At time one the possible states of the world.

Covariance And portfolio variance Review question  Define the internal rate of return.

Quadratic Equations Sum and Product of the Roots.

Many quadratic equations can not be solved by factoring. Other techniques are required to solve them. 7.1 – Completing the Square x 2 = 20 5x =

7.1 – Completing the Square

Solving Quadratic Equations by FACTORING

Do you remember… How do you simplify radicals? What happens when there is a negative under the square root? What is i? What is i 2 ? How do you add or.

Measuring Returns Converting Dollar Returns to Percentage Returns

3 - 1 Risk and Return in Capital Budgeting. Risk And Return of A Single Asset Risk refers to the variability of expected returns associated with a given.

Solving Review Semester 2. Notice the variable is in the exponent. That means we need to use logs to solve. Because an “e” is involved we must use ln.

Q1 The following expression matches the interest factor of continuous compounding and m compounding. Plug r=0.2, m=4 to get x=0.205.

What are quadratic equations, and how can we solve them? Do Now: (To turn in) What do you know about quadratic equations? Have you worked with them before?

Solution sketches, Test 2 Ordering of the problems is the same as in Version D.

Econ 134A Fall 2012 Test 2 solution sketches Average: points What counts as 100%: points (2 students with 55 points; this also counts as 100%)

McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Portfolio risk and return measurement Module 5.2.

5.6 Quadratic Equations and Complex Numbers

Q1 Use the growing annuity formula and solve for C. Plug in PV=50, r=0.1, g=0.07, T=30. C=4.06.

McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. 5-1 Chapter 5 History of Interest Rates and Risk Premiums.

9.4 factoring to solve quadratic equations.. What are the roots of a quadratic function? Roots (x-intercepts): x values when y = 0 ( ___, 0) How do you.

Solving Quadratic Equations by Factoring. Solution by factoring Example 1 Find the roots of each quadratic by factoring. factoring a) x² − 3x + 2 b) x².

DO NOW: FACTOR EACH EXPRESSION COMPLETELY 1) 1) 2) 3)

Using square roots to solve quadratic equations. 2x² = 8 22 x² = 4 The opposite of squaring a number is taking its square root √ 4= ± 2.

Algebra II Honors POD Homework: p odds, odds (you must use completing the square), and 77, 83 Find all real solutions for the following:

Solving Quadratic Equations. Solving by Factoring.

Binomial Distribution Derivation of the Estimating Formula for u an d ESTIMATING u AND d.

Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring.

Chapter 10.7 Notes: Solve Quadratic Equations by the Quadratic Formula Goal: You will solve quadratic equations by using the Quadratic Formula.

Factor. 1)x² + 8x )y² – 4y – 21. Zero Product Property If two numbers multiply to zero, then either one or both numbers has to equal zero. If a.

Making graphs and solving equations of circles.

5-5 Solving Quadratic Equations Objectives:  Solve quadratic equations.

Pre-Calculus Lesson 5: Solving Quadratic Equations Factoring, quadratic formula, and discriminant.

The Quadratic Formula Students will be able to solve quadratic equations by using the quadratic formula.

Do Now 1) Factor. 3a2 – 26a + 35.

Standard 20 The Quadratic Formula Example with numbers put in.

AP Statistics Chapter 16. Discrete Random Variables A discrete random variable X has a countable number of possible values. The probability distribution.

  Different types of Quadratics:  GCF:  Trinomials:  Difference of Squares:  Perfect Square Trinomials: Factoring Quadratics.

Solve by factoring. x² = - 4 – 5x 2,. Solve by factoring. n² = -30 – 11n -4 and -1.

5-7: COMPLEX NUMBERS Goal: Understand and use complex numbers.

Quadratic Formula. Solve x 2 + 3x – 4 = 0 This quadratic happens to factor: x 2 + 3x – 4 = (x + 4)(x – 1) = 0 This quadratic happens to factor: x 2.

1 1. Order alternatives from lowest to highest initial investment. 2. Let Alternative A 0 (do nothing) be considered the current best. 3. Consider next.

Section )by graphing (using the calculator to identify the roots (x-intercepts)) 2)by factoring 3)by “completing the square” 4)by Quadratic Formula:

Markowitz Model 1.  It assists in the selection of the most efficient by analyzing various possible portfolios of the given securities. By choosing securities.

Solving Quadratic Equations. Find the quadratic equation if the solutions are 3 and -2. x = 3 x = -2 Make them equal zero. x – 3 = 0x + 2 = 0 (x – 3)(x.

Algebra 3 Lesson 2.6 Objective: SSBAT solve quadratic equations. Standards: M11.D

1 Topic 27: Investment Returns  Arithmetic average: sum/n  Geometric mean: Less than arithmetic as it factors in compounding As standard deviation increases,

Chapter McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. 11 Diversification and Risky Asset Allocation.

Solving Quadratic Equations by the Complete the Square Method

Warm up – Solve by Taking Roots

Questions-Risk, Return, and CAPM

Question 1a Given: We have a stock that will pay $14 per year with the next dividend paid later today. In 3 years, company can retain all earnings and.

Solving quadratic equations

SECTION 9-3 : SOLVING QUADRATIC EQUATIONS

Solving Quadratic Equations by Factoring

Quadratic Equations.

Completing the Square Algebra Review.

And portfolio variance

Solving Quadratic Equations by Factoring

And portfolio variance

Presentation transcript:

Q1 The discount rate for the value of the option is the expected return on the stock: E(s) =r=0.02+3( )=0.26 The call option has a positive value if (up, up) occurs. This happens with probability: Pr(up,up)=0.6^2=0.36 The present value of the option is: PV=0.36[50(1.15^2)-55]/( )=2.52

Q2 The present value of the cost for r=EAIR=(1.005)^12-1= is: PV=80/(1+r) /(1+r) /(1+r) /(1+r) /(1+r) /(1+r) /(1+r) /(1+r) 27 = The present value of the deposits for the same discount rate: PV=100/(1+r) 2 +x/(1+r) 10 Set the present value of the cost equal to the value of the deposits and solve of x =88.19+x/(1+r) 10 X=133,052

Q3 Calculate the present value of the cash value of dividends for each year and add them together: PV 1/2 =5.5/1.16 1/2 + PV 3/2 =5.5(1.15)/1.16 3/2 + PV 5/2 =5.5(1.15 )2/ /2 + PV 7/2 =5.5(1.15) 3 /1.16 7/2 PV 9/2 =5.5(1.15 )4/ /2 + PV 11/2 =5.5(1.15 )5/ /2 + PV 13/2 =5.5(1.15 )5/ (0.16* /2 ) =60.55

Q4 You can find the covariance of the portfolio by multiplying the correlation by the standard deviations of both stocks: Cov(x,y)=0.04*0.12*0.18= Then use the formula for the portfolio variance and take the square root to find the portfolio’s standard deviation: Var p =0.8 2 * *0.8*0.2* * = Std=( ) 1/2 =

Q5 Use the weighted cost of capital equation from Modigliani and Miller (1958) proposition II: R S = /0.6( )=0.18

Q6 Use the condition that IRR is the discount rate (r) that would make the projects NPV=0. Then solve for r using the quadratic formula. 1.Let x=1+r NPV= /x+1500/x 2 =0 5x 2 +6x-15=0 2. Using the quadratic formula x is either x 1 = x 2 = Ignore any negative rates of return r=x 1 -1=0.23

Q7 The yield on a bond is the discount rate (r) that would make the NPV of the bond equal to zero. Use that condition and solve for r using the quadratic formula. 1.Let x=1+r NPV=0 1320/x /x =0 17x 2 -3x-33=0 2. Using the quadratic formula x is either x 1 = x 2 = Ignore any negative rates of return 4.Currently r is the 6 month discount rate. Transform it to an effective annual interest rate: EAIR=(x 1 ) 2 -1=0.203 = 20.3%