108156.pdf

110 Mathematics for Finance provided that the determinant in the denominator is non-zero. The weights depend linearly onμV. Proo ...

Portfolio Management 111 From Proposition 5.9 we can compute the weights in the minimum variance portfolio. Since uC−^1 ∼= [ 1 ...

112 Mathematics for Finance Example 5.11 (3 securities visualised) There are two convenient ways to visualise all portfolios tha ...

Portfolio Management 113 lios containing securities 2 and 3 only lie on the line through (0. 24 , 0 .15) and (0. 25 , 0 .20). ...

114 Mathematics for Finance Figure 5.8 Portfolios without short selling Exercise 5.14 For portfolios constructed with and withou ...

Portfolio Management 115 use. Employing the techniques of Section 5.2, it may be possible to construct portfolios consisting o ...

116 Mathematics for Finance cw′+(1−c)w′′for anyc∈Rand only of such portfolios. Proof By Proposition 5.10 the minimum variance li ...

Portfolio Management 117 the minimum variance portfolio) satisfy the condition γwC=m−μu (5.17) for some real numbersγ>0andμ ...

118 Mathematics for Finance 5.4 Capital Asset Pricing Model ............................... In the days when computers where slo ...

Portfolio Management 119 Figure 5.11 Efficient frontier for portfolios with a risk-free security Since every investor will sel ...

120 Mathematics for Finance Sincewmust satisfy (5.14), it follows thatγ∼= 3 .694 and the weights in the market portfolio are w∼= ...

Portfolio Management 121 α+βKMis called theresidual random variable. The condition defining the line of best fit is that E(ε^2 ...

122 Mathematics for Finance The beta factor is an indicator of expected changes in the return on a particular portfolio or indiv ...

Portfolio Management 123 for some numbersγ>0andμ. The beta factor of the portfolio with weights wV can, therefore, be writt ...

124 Mathematics for Finance The CAPM describes a state of equilibrium in the market. Everyone is holding a portfolio of risky se ...

6. Forward and Futures Contracts............................. 6.1 Forward Contracts........................................ Afor ...

126 Mathematics for Finance delivery areS(T)−F(0,T) for a long forward position andF(0,T)−S(T)for a short position; see Figure 6 ...

Forward and Futures Contracts 127 Proof We shall prove formula (6.1). Suppose thatF(0,T)>S(0)erT. In this case, at time 0 ...

128 Mathematics for Finance Exercise 6.2 Suppose that the price of stock on 1 April 2000 turns out to be 10% lower than it was o ...

Forward and Futures Contracts 129 Proof Suppose that F(0,T)>[S(0)−e−rtdiv]erT. We shall construct an arbitrage strategy. At ...