Real and Nominal Savings


Kevin Crotty
BUSI 448: Investments

Where are we?

Last time:

  • Saving for retirement

Today:

  • Real and nominal cash flows and rates
  • Uncertainty in returns

Saving for retirement with inflation

Saving for retirement with inflation

  • Now assume we consume a constant real amount in retirement
    • our standard of living will be unchanged each year
  • Can finance with constant nominal or real saving
  • Assume a nominal rate of 5% and inflation of 2% each year

Q1: How much do we need to save each year if saving a constant real amount?

Q2: How much do we need to save each year if saving a constant nominal amount?

Real and Nominal Cash Flows

What is the relationship between real and nominal cash flows at a point in time \(t\)?

\[ \text{Nominal CF}_t = \text{Real CF}_t \cdot (1+\text{inflation})^t. \]

What does the above look like?

Real and Nominal Discount Rates

What is the relationship between real and nominal rates?

\[ 1+ \text{nominal rate} = (1+\text{real rate})(1+\text{inflation}).\]

  • Nominal cash flows are discounted/compounded using nominal rates.
  • Real cash flows are discounted/compounded using real rates.

Uncertain returns

Simulating random returns

We can easily simulate random returns in Python

from scipy.stats import norm
norm.rvs(loc=0.03, scale=0.1, size=50)
  • What does the distribution of ending balances look like if we save $32,000 for 30 years (in real terms) and withdraw $100,000 for 20 years? (both in real terms)
    • Assume real returns are normally distributed with mean of 3% and standard deviation of 10%.
  • How often do we run out of money?!?

For next time: Returns, returns, and more returns…





BUSI 448