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Date Posted: 05:59:26 10/06/00 Fri
Author: Charles Hodges
Subject: Re: NEED HELP WITH MINI CASE
In reply to: Nancy 's message, "NEED HELP WITH MINI CASE" on 20:53:00 10/04/00 Wed

> Please provide solutions to mini-case pg. 198-9-I
> don't have blue prints.Confused about part j and k
> because in order to use SML equation, what is the
> market rate?

Sorry about the all caps. This is a copy/paste from another file.

J. 1. WRITE OUT THE SECURITY MARKET LINE (SML) EQUATION, USE IT TO CALCULATE THE REQUIRED RATE OF RETURN ON EACH ALTERNATIVE, AND THEN GRAPH THE RELATIONSHIP BETWEEN THE EXPECTED AND REQUIRED RATES OF RETURN.
ANSWER: HERE IS THE SML EQUATION:

ki = kRF + (kM - kRF)bi.


IF WE USE THE T-BILL YIELD AS A PROXY FOR THE RISK-FREE RATE, THEN kRF = 8%. FURTHER, FROM THE TABLE, OUR ESTIMATE OF kM = M IS 15%. THUS, THE REQUIRED RATES OF RETURN FOR HIGH TECH ARE AS FOLLOWS.
J. 2. HOW DO THE EXPECTED RATES OF RETURN COMPARE WITH THE REQUIRED RATES OF RETURN?
ANSWER: WE HAVE THE FOLLOWING RELATIONSHIPS:

EXPECTED REQUIRED
RETURN RETURN
SECURITY ( ) (k) CONDITION
___________ ________ ________ _________________________________
HIGH TECH 17.4% 17.0% UNDERVALUED: > k
MARKET 15.0 15.0 FAIRLY VALUED(MARKET EQUILIBRIUM)
U.S. RUBBER 13.8 12.8 UNDERVALUED: > k
T-BILLS 8.0 8.0 FAIRLY VALUED
COLLECTIONS 1.7 2.0 OVERVALUED: k >

THE T-BILLS AND MARKET PORTFOLIO PLOT ON THE SML, HIGH TECH AND U.S. RUBBER PLOT ABOVE IT, AND COLLECTIONS PLOTS BELOW IT. THUS, THE T-BILLS AND THE MARKET PORTFOLIO PROMISE A FAIR RETURN, HIGH TECH AND U.S. RUBBER ARE GOOD DEALS BECAUSE THEY HAVE EXPECTED RETURNS ABOVE THEIR REQUIRED RETURNS, AND COLLECTIONS HAS AN EXPECTED RETURN BELOW ITS REQUIRED RETURN.

J. 3. DOES THE FACT THAT COLLECTIONS HAS AN EXPECTED RETURN WHICH IS LESS THAN THE T-BILL RATE MAKE ANY SENSE?
ANSWER: COLLECTIONS IS AN INTERESTING STOCK. ITS NEGATIVE BETA INDICATES NEGATIVE MARKET RISK--INCLUDING IT IN A PORTFOLIO OF "NORMAL" STOCKS WILL LOWER THE PORTFOLIO'S RISK. THEREFORE, ITS REQUIRED RATE OF RETURN IS BELOW THE RISK-FREE RATE. BASICALLY, THIS MEANS THAT COLLECTIONS IS A VALUABLE SECURITY TO RATIONAL, WELL-DIVERSIFIED INVESTORS. TO SEE WHY, CONSIDER THIS QUESTION: WOULD ANY RATIONAL INVESTOR EVER MAKE AN INVESTMENT WHICH HAS A NEGATIVE EXPECTED RETURN? THE ANSWER IS "YES"--JUST THINK OF THE PURCHASE OF A LIFE OR FIRE INSURANCE POLICY. THE FIRE INSURANCE POLICY HAS A NEGATIVE EXPECTED RETURN BECAUSE OF COMMISSIONS AND INSURANCE COMPANY PROFITS, BUT BUSINESSES BUY FIRE INSURANCE BECAUSE THEY PAY OFF AT A TIME WHEN NORMAL OPERATIONS ARE IN BAD SHAPE. LIFE INSURANCE IS SIMILAR--IT HAS A HIGH RETURN WHEN WORK INCOME CEASES. A NEGATIVE BETA STOCK IS CONCEPTUALLY SIMILAR TO AN INSURANCE POLICY.

J. 4. WHAT WOULD BE THE MARKET RISK AND THE REQUIRED RETURN OF A 50-50 PORTFOLIO OF HIGH TECH AND COLLECTIONS? OF HIGH TECH AND U.S. RUBBER?
ANSWER: NOTE THAT THE BETA OF A PORTFOLIO IS SIMPLY THE WEIGHTED AVERAGE OF THE BETAS OF THE STOCKS IN THE PORTFOLIO. THUS, THE BETA OF A PORTFOLIO WITH 50 PERCENT HIGH TECH AND 50 PERCENT COLLECTIONS IS:
bp = .
bp = 0.5(bHIGH TECH) + 0.5(bCOLLECTIONS) = 0.5(1.29) + 0.5(-0.86)
= 0.215,

kp = kRF + (kM - kRF)bp = 8.0% + (15.0% - 8.0%)(0.215)
= 8.0% + 7%(0.215) = 9.51% . 9.5%.

FOR A PORTFOLIO CONSISTING OF 50% HIGH TECH PLUS 50% U.S. RUBBER, THE REQUIRED RETURN WOULD BE 14.9%:

bp = 0.5(1.29) + 0.5(0.68) = 0.985.
kp = 8.0% + 7%(0.985) = 14.9%.

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Replies:

  • Re: NEED HELP WITH MINI MBA - List of schools/institutions that offer a Mini MBA program -- Ben Hinckfuss, 03:53:48 03/21/02 Thu
  • Re: NEED HELP WITH MINI MBA - List of schools/institutions that offer a Mini MBA program -- Lisa Hatt, 12:06:21 01/02/03 Thu
  • Re: NEED HELP WITH MINI MBA - List of schools/institutions that offer a Mini MBA program -- Kenny Lim, 19:47:06 03/10/03 Mon
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