Monte Carlo> add a new asset question

rich wrote:Under Monte Carlo> build portfolio> add a new asset, I would like to enter my actual mutual fund holdings rather than using the list of “canned assets". Could anyone help me so I am sure I am doing this correctly?
For example,

Vanguard Life Strategy Growth (VASGX)
9.43% = Yearly nominal return since inception before taxes (1994)
13.86 = Standard deviation
1 = R-squared
1.1 = Beta

How do I calculate the answer to question #3 (specify the variance of this asset’s return relative to that of diversified stock)?
Thanks
Rich
Rich,

Variance = Standard Deviation ** 2

It's kind of geeky of us to require you to do that side calculation and I've argued about it, but there you go.

Best,

Dick Munroe

rich wrote:Under Monte Carlo> build portfolio> add a new asset, I would like to enter my actual mutual fund holdings rather than using the list of “canned assets". Could anyone help me so I am sure I am doing this correctly?
For example,

Vanguard Life Strategy Growth (VASGX)
9.43% = Yearly nominal return since inception before taxes (1994)
13.86 = Standard deviation
1 = R-squared
1.1 = Beta

How do I calculate the answer to question #3 (specify the variance of this asset’s return relative to that of diversified stock)?
Thanks
Rich
Rich,

Of course, and here we go...

First thing is find the variance of the rate of return for LCS. I go to our internally maintained data sets, but you can go anywhere you like, the numbers should be approximately the same, and I find that the VAR(LCS) is 0.041087407.

Now, for your asset, the standard deviation is given as 13.86 which I've assumed has been scaled by a factor of 100 but I'll work both numbers.

Variance = standard deviation ** 2

so:

VAR(new) = 13.86 * 13.86 or
VAR(newScaled) = .1386 * .1386 for the scaled case.

Risk = VAR(new) / VAR(LCS) so

RISK(new) = 192.09 / 0.041087407 = 4675.15509071

which seems preposterously high given that you don't also have a preposterously high rate of return, so assuming that the standard deviation was actually scaled by a factor of 100, we get:

RISK(newScaled) = .1386 * .1386 / 0.041087407 = 0.467538873894

which seems out of whack as well since you're getting a pretty good nominal rate of return but it doesn't seem all THAT safe. I'll ask Larry to chime in here, perhaps I'm misunderstanding some of the numbers.

FWIW, if RISK(new) is a correct number, then run screaming because you aren't being rewarded for the level of risk. If RISK(newScaled) is a correct number, then this seems like a pretty good deal (half the risk and better than half the real rate of return).

If you want to figure the real rate of return:

(1 + r) = (1 + n) / (1 + i)

where r = real rate of return, n = nominal rate of return, and i = inflation. In this case you get about a 6.8% real rate of return as compared to a historic 9.11 real rate of return for LCS.

Best,

Dick Munroe

p.s. I'm beginning to see why Harry Truman hated economists...

If the standard deviation was of the nominal rate of return instead of the real rate of return, then the numbers change slightly. In the calculations above, I assumed that the standard deviation was of the real rate of return. If the standard deviation was for the nominal rate of return then the variance that should be used in the above calculations should be: 0.043537608 instead of 0.041087407 and generates an even better deal since the risk becomes 0.4412268125.

The good news is that we're working to develop a tool that will allow you to enter your ticker symbols and get a set of numbers that represent your portfolio as a single asset that can then be fed to the Monte Carlo stuff more or less directly. No time frame yet, but this should get simpler in the future.