Inflation is Much Riskier than Financial Planning Software Makes it out to be

As we’ve learned in recent years, inflation can rise up and make life’s necessities expensive.  Despite the best efforts of central bankers to control inflation through the economic shocks caused by Covid-19, inflation rose significantly for nearly 3 years in both Canada and the U.S.  

Uncertainty about future inflation is an important risk in financial planning, but most financial planning software treats inflation as far less risky than it really is.  This makes projections of the probability of success of a financial plan inaccurate.  Here we analyze the nature of inflation and explain the implications for financial planning.

Historical inflation

Over the past century, inflation has averaged 2.9% per year in both Canada and the U.S.(*)  However, the standard deviation of annual inflation has been 3.6% in Canada and 3.7% in the U.S.  This shows that inflation has been much more volatile than we became used to in the 2 or 3 decades before Covid-19 appeared.  In 22 out of 100 years, inflation in Canada was more than one standard deviation away from the average, i.e., either less than -0.7% or more than 6.5%.(**)  Results were similar in the U.S.

Historical inflation has been far wilder than the tame inflation we experienced from 1992 to 2020.  And the news gets worse.  Within reason, a single year of inflation is not a big deal to a long-term financial plan; what matters is inflation over decades.  It turns out that inflation is wilder over decades than we’d expect by examining just annual figures with the assumption that each year is independent of previous years.

The standard deviation of Canadian inflation over the twenty 5-year periods is 14%, and over the ten decades is 27%.  Based on assuming independent annual inflation amounts, we would have expected these standard deviation figures to be only 8% and 11%.  How could the actual numbers be so much higher?  It turns out that inflation goes in trends.  This year’s inflation is highly correlated with last year’s inflation.  Rather than a correlation of zero, the correlation from one year to the next is 66% in Canada and 67% in the U.S.(***)

Even successive 5-year inflation samples have a correlation of 60% in Canada and 56% in the U.S.  It’s only when we examine successive decades of inflation that correlation drops to 23% in Canada and 21% in the U.S.  This is low enough that we could treat successive decades of inflation as independent, but we can’t reasonably do this for successive years.

How relevant is older inflation data?

Some might argue that old inflation data isn’t relevant; we should use recent inflation data as more representative of what we’ll see in the future.  After all, central banks had a good handle on inflation for a long time.  Let’s test this argument.

From 1992 to 2020, inflation in Canada averaged 1.72% with a standard deviation of 0.94%.  Using this period as a guide, the inflation that followed was shocking.  In the 32 months ending in August 2023, inflation was a total of 15.5%.  Using the 1992 to 2020 period as a model, the probability that the later 32 months could have had such high inflation is absurdly low: about 1 in 10 billion.(****)

It may be that older inflation data is less relevant, but our recent bout of inflation proves that the 1992 to 2020 period cannot reasonably be used as a model for future inflation.  There is room for compromise here, but any reasonable model must allow for the possibility of future bouts of higher inflation.

Implications

It’s important to remember that once a bout of inflation has been tamed, the damage is already done.  Prices have jumped quickly and will start climbing slower from their new high levels.  If there has been 10% excess inflation over some period, all long-term bonds and future annuity payments will be worth 10% less in real purchasing power than our financial plans anticipated.  This is a serious threat to people’s finances.

We often hear that government bonds are risk-free if held to maturity.  This is only true when we measure risk in nominal dollars.  Because spending rises with inflation, our consumption is in real (inflation-adjusted) dollars.  Bonds held to maturity are exposed to the full volatility of inflation.  We need to acknowledge that bonds have significant risk.  Only inflation-protected government bonds are free of risk.

When financial planning software uses a fixed constant for inflation, like 2% or 2.5%, it is understating the risk posed by inflation.  With constant inflation, bonds held to maturity look risk-free when they aren’t.

Most annuities are also exposed to inflation risk.  Annuities are good for removing longevity risk, but future payments are not as stable in real dollars as they appear to be in nominal dollars.

When software performs Monte Carlo simulations to determine the probability that a financial plan will fail, a poor model of inflation overstates the protection offered by bonds and annuities.  The probability that bonds and annuities will fail to perform their main function of providing safety is higher than these simulators estimate.

It’s fairly easy to write software that performs Monte Carlo portfolio simulations.  The challenge is in correctly modelling investment returns and inflation with reasonable parameters.  Unfortunately, software outputs look equally slick whether this modelling is done well or not.  It’s easy to tinker with model parameters to get the success percentage you want for a financial plan, even if you don’t intend to cheat.

Remedies

One way to address inflation risk is to model it better and simulate it along with stock and bond return simulations.  However, stock and bond returns are not independent of inflation.  If a particular simulation run has high inflation, it’s not reasonable to assume that subsequent nominal stock and bond returns are unaffected.

Along with high inflation, we often get interest rate changes, which affects future bond returns.  Businesses typically raise prices in response to inflation, which can raise future nominal stocks returns.  The interplay between inflation and investment returns is complex.

Some financial planners recognize the problem of fixed inflation assumptions and they run their Monte Carlo simulations with different fixed values for future inflation as a further test of a financial plan.  This helps to some degree, but they are punishing the returns from bonds, annuities, and stocks equally, which doesn’t reflect the reality of inflation’s effects on different types of investment returns.

Because we spend real inflation-adjusted dollars, it’s better to model the real returns of stocks, bonds, and other investments directly.  Instead of studying nominal stock returns to create simulation models, we should study and model real stock returns.  The same is true for bonds and other types of investments such as real estate.

We would still need to model inflation to estimate capital gains taxes and anything else that is based on nominal dollars, but directly modelling the real returns of investments tends to make it easier to properly simulate and test a financial plan.

Conclusion

Most financial planning software underestimates the potential for inflation to disrupt a financial plan.  Measuring volatility in nominal terms is fundamentally misguided, and treating inflation as constant implicitly treats nominal and real quantities as having the same volatility.  As a result of this distortion, bonds and annuities are over-valued as a means to control risk.  Inflation-protected bonds are under-valued.  The success percentages that portfolio simulators calculate for financial plans often have little connection to reality.

Footnotes

(*) All figures used here use the logarithm of Consumer Price Index (CPI) ratios.  This is important for good modelling of inflation and investment returns, but makes only a modest difference in the actual figures.  For example, the average logarithm of annual inflation in Canada for the past century is 2.914%, which corresponds to compound average annual inflation of exp(2.914%)-1=2.957%.

(**) For those who expected inflation to be more than one standard deviation from its mean 32% of the time instead of 22%, this is misapplying the normal distribution (also known as the bell curve).  Inflation figures are far from normally distributed.  Financial mathematics is littered with over-application of the normal distribution.

(***) When a random variable is uncorrelated with its past annual values, the standard deviation of a 5-year sum is sqrt(5) times the standard deviation of a single year.  For decades, we multiply by sqrt(10).  With inflation, the actual correlation is not zero; the autocorrelation coefficient is about 2/3.

(****) Assuming that annual inflation samples are independent and lognormal with a mean of 1.72% and standard deviation of 0.94%, our recent 32-month bout of inflation is a 6.4-sigma event, which has probability of about 10^(-10).  So, the distribution assumptions are clearly not true.