portfolio question- pls guide question, expected, standard, returns

bodhisattva

1.      Determine the expected value and standard deviation of the returns of portfolio X and Y. Each of the two assets holds equal weights i.e. 50% each. The table below states the forecasted returns of both assets.
Year
Forecasted Returns
Asset X
Asset Y
2010
12%
16%
2011
11%
18%
2012
14%
12%
2013
16%
8%
2014
14%
10%

morebeans

this is one of the easiest possible questions you could ever hope to get!  if you see this on the exam it will be a gift.  Just look up the definitions of how to compute expected return and standard deviation, for example expected return is the sum of weighted average returns, for 2010 that would be 0.5*12% + 0.5*16% etc.  you can do this for each year then compute the average expected return and use that for the standard deviation calculation…

soverby

yup, it is easy,  my answers are avg return -13.1% and std dev -0.01019.. however, does not tally.. hence I thought I might have missed something

malbec

How are you getting a negative std deviation? that is not possible.
is
std dev =0.011402?

cchang

Could you pose the question more precisely?
I assume you are supposed to estimate the expected return and the standard deviation of the portfolio comprising assets X and Y and each asset’s weight is 0,5. Am I right?
In this case you need to estimate the covariance of the asset return in order to calculate the portfolio standard deviation.
Quote:yup, it is easy,  my answers are avg return -13.1% and std dev -0.01019.. however, does not tally.. hence I thought I might have missed something
Not so easy as it seems.
Just by looking at the numbers we can see that the expected returns of both assets will be positive double digits.
E[X] = 0,134;  St. dev.[X] = 0,0194
E[Y] = 0,128;  St. dev.[Y] = 0,0414
Correlation coefficient bet. XY =  -0,977
E[P] = 0,1198; St. dev. [P] = 0,01141

JonnyKay

that’s a good answer but not necessary to get that complex.  just compute the portfolio return for each year then take the average value, the average is 13.1% as noted elsewhere.  then, compute the square of the annual return - this average for each year.  divide that by the number of observations -1, take the square root and you have 1.1402%.

Year X Y Portfolio (port-mean)^2
2010 12% 16% 14% 8.1E-05
2011 11% 18% 15% 0.000196
2012 14% 12% 13% 0.000001
2013 16% 8% 12% 0.000121
2014 14% 10% 12% 0.000121
mean 13.4% 12.8% 13.1% 1.1402%