EBK INVESTMENTS
EBK INVESTMENTS
11th Edition
ISBN: 9781259357480
Author: Bodie
Publisher: MCGRAW HILL BOOK COMPANY
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 21, Problem 45PS
Summary Introduction

(A)

Adequate Information:

The portfolio you manage is currently worth $100 million, and you promise to provide a minimum return of 0%. The equity portfolio has a standard deviation of 25% per year, and T-bills pay 5% per year.

  Current value of portfolio(So)=$100 millionFloor promised to clients. 0% return(X)=$100 millionVolatility(σ)=0.25Risk-free rate(r)=0.05Horizon of program(T)=4 yearsDividend yield (δ)=0

To calculate:

The fraction of the portfolio, fraction in equity and the stock portfolio if falls by 3%.

Introduction:

Portfolio involves financial asset grouping viz. currencies, commodities, bonds, stocks and cash equivalents. It also comprises of fund counterparts such as closed funds, exchange traded funds and mutual funds. Non-publicly tradable securities such as private, art and real estate investment are also part of portfolios.

Expert Solution
Check Mark

Explanation of Solution

Fractions of portfolio invested in T-bills and equity can be calculated based on the Black-Scholes
model. The value of N(d1)defines the normal distribution of portfolio returns. Weighted given
to T-bills and equity can be known for value of N(d1)

Formula for d1 as per Black-Scholes model is as follows:

d1=In( So X)+(rδ+ σ2 2)TσTSo=Currnt stock priceN(d1)and N(d2)=Cumulative normal distribution functionsX=Exercise pricerr= Annualised risk free rated= Annual dividend yield of underlying stocks=Annualised standard deviation of share returnsT = Time to expiry In( S oX)=Natural logarithmic value ofSoX e =Exponential having the constant of 2.71828δ=Annual dividend yield of underlying stockσ=Annualised standard deviation of share returns or Volatility

Substitute values to calculate d1as follows:

So=$100 million,X=$100 million,r=0.05,σ=0.25,δ=0,andT=0d1=In( So X)+(rδ+ σ2 2)TσT=In($100$100)+(0.050+ 0.25 22)4=In(1)+(0.050+0.03125)40.5=In(1)+0.3250.5=0+0.3250.5=0.65

Calculate the Black-Scholes hedge ratio N(d1)of call option using Ms-Excel"NORMSDIST" Function as follows:

EBK INVESTMENTS, Chapter 21, Problem 45PS , additional homework tip  1

N(d1)can be calculated using Excel "NORMSDIST" function. The Excel steps to calculate
"NORMSDIST" function are as follows:

  • First, go to the Menu bar of Excel and select 'Formulas' option
  • Select Insert Function '(fx)
  • Then select a category as Financial
  • Then select "NORMSDIST" and click OK
  • Then the Function Argument window will open. Now, input the given data in the required field
  • Click OK
  • The formula will display the final answer as 0.7422

Therefore, N(d1) value is 0.7422

Calculate the put delte as follows:

  Putdelta=N(d1)1=0.74221=0.2578

Hence, place 25.785 of the portfolio in T-bills and 74.22% (10025.78%)inequity

Conclusion

Hence, place 25.785 of the portfolio in T-bills and 74.22% (10025.78%) inequity and the stock portfolio if falls by 3% will be $1.1763.

Summary Introduction

(B)

Adequate information:

  Current value of portfolio(So)=$97 millionFloor promised to clients. 0% return(X)=$100 millionVolatility(σ)=0.25Risk-free rate(r)=0.05Horizon of program(T)=4 yearsDividend yield (δ)=0

To calculate:

Fractions of portfolio divided into bills and equity If stock prices fall by 3% on the first day of trading. It means So (current value of the portfolio) falls to $97

Introduction:

Portfolio involves financial asset grouping viz. currencies, commodities, bonds, stocks and cash equivalents. It also comprises of fund counterparts such as closed funds, exchange traded funds and mutual funds. Non-publicly tradable securities such as private, art and real estate investment are also part of portfolios.

Expert Solution
Check Mark

Explanation of Solution

Fractions of portfolio invested in T-bills and equity can be calculated based on the Black-Scoles model. The value of N(d1) defines the normal distribution of portfolio returns. Weighted given to T-bills and equity can be known for value of N(d1)

Substitute values to calculate d1as follows

So=$97 million,X=$100 million,r=0.05,σ=0.25,δ=0,andT=4d1=In( So X)+(rδ+ σ2 2)TσT=In($97$100)+(0.050+ 0.25 22)4=In(0.97)+(0.050+0.03125)40.5=In(0.97)+0.08125×40.5=0.0305+0.3250.5=0.29450.5=0.589

Calculate the Black-Scholes hedge ratio N(d1)of call option using Ms-Excel"NORMSDIST" Function as follows:

EBK INVESTMENTS, Chapter 21, Problem 45PS , additional homework tip  2

Hence, N(d1)value is 0.7221.

Calculate the put delta as follows:

  Difference =(Amount of T-bills as per sub-part ( b)Amount of T-bills as per sub-part ( a))=$97 million×27.79%)($100 million×25.78%)=$26.9563$25.78=$1.1763

Conclusion

Hence, place 27.79% of the portfolio in T-bills and 72.21% (10027.79%)in equity. The amount of T-bills is $26.96 million ($97 million×0.2779) .The manager must sell $1.1763 million of equity and use the proceeds to buy bills.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Imagine you are a provider of portfolio insurance. You are establishing a four-year program. The portfolio you manage is currently worth $210 million, and you promise to provide a minimum return of 0%. The equity portfolio has a standard deviation of 25% per year, and T-bills pay 7% per year. Assume for simplicity that the portfolio pays no dividends (or that all dividends are reinvested). a-1. What percentage of the portfolio should be placed in bills? (Input the value as a positive value. Round your answer to 2 decimal places.) Portfolio in bills % a-2. What percentage of the portfolio should be placed in equity? (Input the value as a positive value. Round your answer to 2 decimal places.) Portfolio in equity %
You are a provider of portfolio insurance and are establishing a four-year program. The portfolio you manage is currently worth $190 million, and you promise to provide a minimum return of 0%. The equity portfolio has a standard deviation of 25% per year, and T-bills pay 5.5% per year. Assume that the portfolio pays no dividends. a-1. How much of the portfolio should be sold and placed in bills? a-2. How much of the portfolio should be sold and placed in equity? b-1. Calculate the put delta and the amount held in bills if the stock portfolio falls by 3% on the first day of trading, before the hedge is in place? b-2. What action should the manager take?
You are a provider of portfolio insurance and are establishing a four-year program. The portfolio you manage is currently worth $70 million, and you promise to provide a minimum return of 0%. The equity portfolio has a standard deviation of 25% per year, and T-bills pay 6.2% per year. Assume that the portfolio pays no dividends.   Required: a-1. How much of the portfolio should be sold and placed in bills? (Input the value as a positive value. Do not round intermediate calculations and round your final percentage answer to 2 decimal places.)   a-2. How much of the portfolio should be sold and placed in equity? (Input the value as a positive value. Do not round intermediate calculations and round your final percentage answer to 2 decimal places.)   b-1. Calculate the put delta and the amount held in bills if the stock portfolio falls by 3% on the first day of trading, before the hedge is in place? (Input the value as a positive value. Do not round intermediate calculations. Round your…
Knowledge Booster
Background pattern image
Finance
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Essentials Of Investments
Finance
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Mcgraw-hill Education,
Text book image
FUNDAMENTALS OF CORPORATE FINANCE
Finance
ISBN:9781260013962
Author:BREALEY
Publisher:RENT MCG
Text book image
Financial Management: Theory & Practice
Finance
ISBN:9781337909730
Author:Brigham
Publisher:Cengage
Text book image
Foundations Of Finance
Finance
ISBN:9780134897264
Author:KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:Pearson,
Text book image
Fundamentals of Financial Management (MindTap Cou...
Finance
ISBN:9781337395250
Author:Eugene F. Brigham, Joel F. Houston
Publisher:Cengage Learning
Text book image
Corporate Finance (The Mcgraw-hill/Irwin Series i...
Finance
ISBN:9780077861759
Author:Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher:McGraw-Hill Education
Portfolio Management; Author: DevTechFinance;https://www.youtube.com/watch?v=Qmw15cG2Mv4;License: Standard YouTube License, CC-BY