# Simple simulation model of bond plus cash returns

Is there a robust way to model 'bond plus cash' simulated returns, say in Excel, for an asset allocation problem between stocks vs bond plus cash?

For equity, mean 5% st dev 15% I would use X=U~[0,1] and R=N(X)~[0.05,0.15^2].

For bond, mean 3% st dev 6%, and for cash mean 2% st dev 2%.

The question is then two-fold:

• How do I easily truncate cash returns at 0
• How do I combine the return-risk assumption for both risk-less instruments.
• Are you saying that cash and bonds are riskless because, although there is a standard deviation, you are capping the loss at 0? This problem seems very unrealistic, so I would appreciate more details. Is there an original question? – RandyF Dec 1 '16 at 21:36
• No original. I'm making no assumptions on risky or risklessness. This is a question about simulations (say 5000,10000) given a distribution and what the distribution should be. Consider a DC pension lifestyling strategy that starts 100% equity and ends 0% eq 100% bond and cash at NRD. – rrg Dec 2 '16 at 8:37
• So, you want to have a varying percentage of equity and bonds through time? If so, how do you plan to shift from equity to bonds? I ask because this shift moves from requiring a 2d matrix of random numbers (2d if returns are dependent on each other; if independent, this can be done with 2 closed form equations) to a 3d matrix (a 2d matrix for each asset). – RandyF Dec 2 '16 at 15:23
• @RandyF not bothered about modelling the equity interdependence/covariance, forget it exists - just a bond/cash sketch as per qn. – rrg Dec 2 '16 at 15:56

$$weight_{eq} * (0.05 + 0.15 * rand()) + weight_{bnd} * (0.03 + 0.06 * rand()) + weight_{cash} * (0.02 + 0.02 * rand())$$
$$\frac{50-year}{50} (0.05 + 0.15 * rand()) + \frac {year}{50} (0.03 + 0.06 * rand()) + \frac {year}{50} (0.02 + 0.02 * rand())$$
• It should be $(1+r_1)*(1+r_2)*...*(1+r_n) - 1$ with correct compounding. $r_1+r_2+...+r_n$ can be very far off as the total term increases. – RandyF Dec 9 '16 at 19:31