1. Suppose that there are two independent economic factors,F₁andF₂. The risk-free rate is 6%, and all stocks have independent firm-specific components with a standard deviation of 45%. The following are well-diversified portfolios:

Portfolio	Beta onF1	Beta onF2	Expected Return
A	1.5	2.0	31%
B	2.2	0.2	27%

What is the expected returnbeta relationship in this economy?(Do not round intermediate calculations. Omit the "%" sign in your response.)

E(r_P) =?% + (_P1?%) + (_P2?%) please solve all the "?"

2.

Assume that security returns are generated by the single-index model,

R_i=_i+_iR_M+e_i

whereR_iis the excess return for securityiandR_Mis the markets excess return. The risk-free rate is 2%. Suppose also that there are three securitiesA,B, andC, characterized by the following data:

Security	i	E(Ri)	(ei)
A	0.8	10%	25%
B	1.0	12	10
C	1.2	14	20

a.	IfM= 20%, calculate the variance of returns of securitiesA,B, andC.(Do not round intermediate calculations. Round your answers to the nearest whole number.)

	Variance
SecurityA	?
SecurityB	?
SecurityC	?

b.

Now assume that there are an infinite number of assets with return characteristics identical to those ofA,B, andC, respectively. What will be the mean and variance of excess returns for securitiesA,B, andC?(Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number. Omit the "%" sign in your response.)

	Mean	Variance
SecurityA	?%	?
SecurityB	?%	?
SecurityC	?%	?

slove all the "?" as well please show all the works, thak you here I upload the fomula sheet for you thank you

Economics 106V: Midterm Formula Sheet F V = P V (1 + r)t (Future Value) (1) Ct (1 + r)nt (Future Value of a Cash Flow Stream) (2) n F Vt = t=0 n PV = t=0 PV = Ct (Present Value of a Cash Flow Stream) (1 + r)t C r 1 (1 + r)n (3) (Present Value of an Annuity) (4) (Present Value of a Perpetuity (5) AP R = nr (Annual Percentage Rate (6) EAR = (1 + AP R)n 1 (Eective Annual Rate) (7) EAR = eAP R 1 (Eective Annual Rate -Continuous Compounding) (8) F V = P V ert (Future Value -Continuous Compounding) (9) Accumulated Value 1 (Holding-Period Return) Starting Value (10) aHP R = (1 + HP R)1/t 1 (Annualized Holding-Period Return) (11) 1 C r PV = HP R = Arithmetic Average = 1 T T HP Rt (12) t=1 T (1 + HP Rt )1/T Geometric Average = 1 (13) Ct (Internal Rate of Return) (1 + IRR)t (14) t=1 P (0) = t=1 N i Ri (Return on Portfolio P ) (15) i E[Ri ] (Expected Return on Portfolio P ) (16) Cov(X, Y ) = E[(X E[X])(Y E[Y ])] (Covariance) (17) Cov(X, Y ) (Correlation) X Y (18) RP = i=1 N E[RP ] = i=1 X,Y = -2- N N 2 P 2 2 i i i j i,j i j , (Portfolio Variance) (19) 2 2 2 2 2 P = 1 1 + 2 2 + 21 2 1,2 1 2 , (Portfolio Variance -Two Securities) (20) E[RP ] = E[R1 ] + (1 )E[R2 ] (Portfolio Expected Return -Two Securities) (21) 2 2 2 P = 2 1 + (1 )2 2 + 2(1 )cov(R1 , R2 ) (Portfolio Variance -Two Securities) (22) E[Ri ] Rf (Sharpe Ratio) i (23) E[RP ] = Rf + P (E[Ri ] Rf )/i (Capital Allocation Line) (24) 1 M cov(Ri , RT ) or i = (Beta of a Stock) 2 M i T (25) E[Ri ] = Rf + i,T (E[RT ] Rf ) (Risk-Return Relationship -Tangency Portfolio) (26) = +2 i=1 j>i i=1 SRi = i,T = 2 P = 1 1 2 + 1 N N cov(Ri , Rj ) (Portfolio Variance -N -Independent Assets) (27) Ri (t) = i + i RM (t) + ei (t) (Single-Index Model) (28) E[RP ] = Rf + P (E[RM ] Rf )/M (Capital Market Line) (29) E[Ri ] = Rf + i (E[RM ] Rf ) (Security Market Line) (30) Ri Rf = i + i (RM Rf ) + i (Security Characteristic Line) (31) 2 i Total Risk = 2 2 i M Market Risk + 2 i Idiosyncratic Risk (32)