# Monte Carlo scenario generation

RightCapital is known for "financial advising done just right." Highly sophisticated projections are a critical key in being able to do excellent financial planning. RightCapital uses advanced Monte Carlo simulations for all future-date predictions, such as in the Retirement Analysis tool.

RightCapital's Monte Carlo simulations generate 1,000 return scenarios to illustrate potential paths for the client's financial future.

#### Custom Asset Classes

For advisors using Custom Asset Class capabilities, a slightly different model is used. This is due to the immense power of utility RightCapital places in the hands of these advisors, including the ability to update standard deviation/correlation assumptions. This granular approach utilizes a standard log-normal distribution model.

The Monte Carlo simulation uses the global asset class returns, applied to the Proposed Asset Allocation model indicated in the Retirement Analysis Action Items.

**Equity returns modeling**

Our standard Monte Carlo simulation model uses a stochastic volatility model that is often used in banks and life insurance companies to capture the dynamics of equity returns. The three key features that a stochastic volatility model brings to retirement planning include the following:

**Fat tails.**A typical lognormal model or model with t-distribution cannot generate an adequate amount of fat tails. That is the returns in the bad scenarios are usually not bad enough. In statistical terms, fat tails are negative skewness and positive kurtosis. A stochastic volatility model is capable of capturing this. This is extremely important for retirement planning. If a simple lognormal or t-distribution model is used; it could significantly underestimate the tail scenarios and overestimate the probability of success.**Volatility as a random process**and accurate representation of volatility clustering. Volatility is not constant. A typical lognormal model assumes constant volatility and cannot be used for retirement planning. A stochastic volatility model will capture the variances in volatility.**Increased volatility in a bad market.**Empirical results have shown that in a stressful equity market, the volatility tends to increase. In a more favorable market, the volatility tends to decrease. A stochastic volatility model will incorporate the correlation between equity and volatility. This will accurately capture the increased volatility in a bad market.

**Bond returns modeling**

RightCapital utilizes a realistic model which is often used in banks and insurance companies to capture a realistic development of fixed income returns. The model has a very intuitive explanation. The monthly return of the bond has three components:

- An interest rate component which is equal to (treasury rate + credit spread) for one month
- A price return component which is equal to the change in interest rate multiplied by the duration of the bond
- A random noise component with an expected value of zero that introduces volatility

The money market index assumes a function of the 3-month yield. Government bonds assume a 7-year maturity and corporate bonds assume a 10-year maturity. Fixed income index assumes a 65% government and 35% corporate split.