Capital-Asset-Pricing : Based on the capital-asset-pricing model, what is the expected return on the above portfolio?

Suppose you have invested $50,000 in the following four stocks: Security Amount Invested Beta Stock A $10,000 0.7 Stock B 15,000 1.2 Stock C 12000 ...continues

What is the forward price of your contract? b. Suppose both the spot rates unexpectedly shift downward by 1 percent. What is the price of a forward contract otherwise identical to yours?

You enter into a forward contract to buy a 10 year, zero-coupon bond that will be issued in one year. The face value of the bond is $1000, and the 1-year spot interest rates are 4 percent per annum at 9 percent per annum, respectively. Both of these interest rates are expressed as effective annual yields (EAYs). a. What is ...continues

Accounting, face value of bonds sell for

9. How much should a $1,000-face-value bonds sell for, assuming the following conditions: The bond pays a coupon of 11% The coupon payments are paid annually. The required rate of return on similar-risk investments is 9%. The bond matures in 15 years 10. How much should a $1,000-face-val ...continues

Numerical Linear Algebra. Norms.

Find two norms on the space C[0,1] that are not equivalent. Justify your answer. ( Please prove that the example you provide is a norm on the given space and show that the 2 are not equivalent.)

Numerical linear algebra/norms

Based on the parallelogram law, show that the norms ||.||_1 (1-norm) and ||.||_infinity ( infinity or maximum norm) in R^2 are not induced by any inner product. Parallelogram Law: ||u+v||^2 + ||u-v||^2 = 2||u||^2 + 2||v||^2. ||x||_1: = sum i = 1 to n of |x_i| ||x||_infinity := max ( 1 =< i =< n)|x_i|

Numerical Linear Algebra. Neuman Lemma.

Prove the Neuman Lemma: if ||A|| < 1, then I - A is invertible. Here ||.|| is a norm on the space of nxn matrices induced by a norm on R^n or C^n ( C is complex plane). I want a detailed proof. Thanks.

Subspace of Inner Product Space and Finite Dimensional Space

1. (i) Let W C V be a subspace of an inner product space V . Prove that W C (W) . (ii) If, in addition, V is finite dimensional, prove that W = (W). Please see the attached file for the fully formatted problems.

Orthogonal Matrix : Eigenvalues and Eigenvectors

Show that if Q be a real orthogonal 2×2 matrix and detQ = −1, then Q = (cos θ sin θ) (sin θ −cos θ) for some θ E 2 [0, 2pi). Then prove that λ = ±1 are eigenvalues of the above matr ...continues

Orthogonal Matrix and Eigenvalues : Let A be a 3 x 3 real orthogonal matrix with det A = 1. Prove that λ= 1 is an eigenvalue of A.

Let A be a 3 x 3 real orthogonal matrix with det A = 1. Prove that λ= 1 is an eigenvalue of A.

Gram-Schmidt Orthogonalization ( Orthonormalization ) and Inner Product

Apply Gram-Schmidt orthonormalization to the the basis {1, x, x2} in the space P2(R) with the inner product = ∫ 0-->1 f(x)g(x) dx Don't worry about the extra credit part. Please see the attached file for the fully formatted problems.