Question

Stocks A and B have the following returns Stock B Stock A 0.1 007 004 2 34 0.04 0.12 0.06 4 004 003 5 0.08 0.04 a. What are the expected returns of the two stocks? b What are the standard deviations of the returns of the two stocks? e. If their comelation is 0.43 what is the expected return and standard deviation of a portfolio of 60% stock A and 40% stock B? a. What are the expected returns of the two stocks? The expected return for stock A is(Round to three decimal places) The expected return for stock B is (Round to three decimal places.) b. What are the standard deviations of the returns of the two stocks? The standard deviation of the retun for stock A is (Round to four decimal places) (Round to four decimal places.) The standard deviation of the return for stock B is e, If their comrelation is 043 what is the expected return and standard deviation of a portfolio of 60 % stock A and 40% stock B? The expected return for the portfolio is(Round to four decimal places) (Round to four decimal places) The standard deviation of the retun for the portfolio is

please help

Answer 1

Expected or Average return = Sum of returns/no. of periods          
Standard deviation = √ (∑ (Return- Expected return)^2)/(no. of periods - 1))          
Stock A          
   R   R- ER (ER = 0.062)   (R-AR)^2
1   0.11   0.0480   0.002304
2   0.04   -0.0220   0.000484
3   0.12   0.0580   0.003364
4   -0.04   -0.1020   0.010404
5   0.08   0.0180   0.000324
          
          
Total    0.31       0.01688
Expected Return = 0.31/5 =   0.0620      
          
Standard deviation = √(0.01688/(5-1))          
0.06496152708          
          
          
Stock B          
   R   R- ER (ER = 0.032)   (R-AR)^2
1   0.07   0.0380   0.001444
2   0.04   0.0080   0.000064
3   0.06   0.0280   0.000784
4   0.03   -0.0020   0.000004
5   -0.04   -0.0720   0.005184
          
          
Total    0.16       0.00748
Expected Return = 0.16/5 =   0.0320      
          
Standard deviation = √(0.00748/(5-1))          
0.04324349662          
          
Expected return of A   0.062      
Expected return of B   0.032      
Standard deviation of A   0.0650      
Standard deviation of B   0.0432      
Correlation   0.43      
Weight of A   60%      
Weight of B   40%      
          
Expected return of Portfolio= (weight of A * Expected return of A) + (Weight of B * Expected retun of B)          
(60%*0.062)+(40%*0.032)          
0.0500          
So Expected Return of Portfolio is 0.0500          
          
          
Standard deviation (σp) formula=√ ( (wA * σA ) ^2 + (wB * σB ) ^2 +( 2 * wA* wS*Cov AB )          
√((60%*0.06496152708)^2+(40%*0.04324349662)^2+(2*60%*40%*0.06496152708*0.04324349662*0.43))^0.5          
0.0490          
          
So standard deviation of portfolio is 0.0490          

377 378 379 380 381 382 383 384 Expected or Average return = Sum of returns/no. of periods Standard deviation = ( (Return-Expected return) 2)/(no. of periods - 1 Stock A R R-ER (ER = 0.C (R-AR)^2 1 0 .11 0.0480 0.002304 2 0 .04 -0.0220 0.000484 3 0 .12 0.0580 0.003364 -0.04 -0.1020 0.010404 5 0.08 0.0180 0.000324 385 386 387 388 389 390 0.01688 391 392 Total Expected Return 0.31 0.0620 393 Standard deviation = V(0.01688/(5-1)) 0.06496152708 394 395 396 397 398 399 Stock B 400 401 R-ER (ER = 0.C (R-AR)^2 0.07 0.0380 0.001444 0.04 0.0080 0.000064 0.06 0.0280 0.000784 0.03 -0.0020 0.000004 -0.04 -0.0720 0.005184 402 403 404 405 406 0.00748 407 Total 0.16 408 Expected Return 0.0320 409 410 Standard deviation = v(0.00748/(5-1)) 411 0.04324349662 fx So standard deviation of portfolio is 0.0490

412 413 Expected return 0.062 414 Expected return 0.032 415 Standard deviatic 0.0650 416 Standard deviatic 0.0432 417 Correlation 0.43 418 Weight of A 60% 419 Weight of B 40% 420 421 Expected return of Portfolio= (weight of A* Expected return of A) + 422 (60%*0.062)+(40%*0.032) 423 0.0500 424 So Expected Return of Portfolio is 0.0500 425 426 427 428 429 Standard deviation (op) formula= ((WA* OA)^2 + (WB * OB)^2 + ? N((60%*0.06496152708)^2+(40%*0.04324349662)^2+(2*60%*40%*0.06496 0.0490 430 So standard devlation of portfolio is 0.0490 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 fx So standard deviation of portfolio is 0.0490