Financial Planning - Investments: Risk and Return

Learning Objectives

• Determine present and future values of cash flows.
• Explain the impact of compounding.
• Understand nominal vs. effective interest rates.
• Explain why risk measures are important.
• Identify types of investment risks.
• Describe portfolio risk determination.
• Identify risk characteristics of asset classes.
• Understand diversification as a risk-reduction strategy.
• Appreciate client characteristics.

Introduction

• Financial planning requires knowledge across diverse areas.
• Technical skills are required (investments, compounding, risk, returns, diversification).
• Financial planners need strong math skills for investment and retirement planning.
  • Compound interest.
  • Time value of money.

Time Value of Money

• A dollar today is worth more than a dollar in the future.
  • Risk/uncertainty of future collection.
  • Opportunity cost.
  • Postponement of consumption.

Time Value Terminology

• n = Number of time periods.
• i = Interest rate.
• PV = Present Value.
• FV = Future Value.
• All time value questions involve four values: PV, FV, i and n. Given three of them, it is always possible to calculate the fourth.

Time Line – Compounding & Discounting

• Future value (FV) measures cash flows at the END of the project’s life
• Present value (PV) measures cash flows at the BEGINNING of the project’s life

Terminology

• Simple interest: interest calculated only on the original principal.
• Compound interest: interest calculated on the balance as income is reinvested.
• Nominal interest rate: annual rate without considering compounding frequency.

Simple Interest

• Formula: $I = PV \times i \times n$, where:
  • I = Interest amount
  • PV = Present value
  • i = Interest rate per annum (decimal)
  • n = Number of days cash is on deposit / 365

Future Values

• Formula: $FV = PV + I = PV + (PV \times i \times n) = PV (1 + in)$

Present Value of a Future Amount

• Formula: $PV = \frac{FV}{(1 + in)}$

Compound Interest

• Interest is calculated on the outstanding balance, reinvesting income.
• Future Value Formula: $FV = PV(1 + i)^n$
  • FV = future value
  • PV = present value
  • i = interest rate per period
  • n = number of periods

Present Value Compound Interest

• Formula: $PV = \frac{FV}{(1 + i)^n}$

Nominal and Effective Interest Rates

• Nominal rate: Stated interest rate.
• Effective rate: Real rate after adjusting for compounding frequency.
• Periodic interest rate: $i = \frac{j}{m}$, where j is the annual interest rate, and m is the number of compounding periods.
• Effective Interest Rate : $i_e = (1 + \frac{i}{m})^m -1$

Annuities

• A stream of equal periodic cash flows over a specified period
• Characteristics:
  • fixed term to maturity
  • regular stream of equal payments
• Types of annuity:
  • Ordinary annuity: paid at the end of each period
  • Annuity due: paid at the beginning of each period
  • Deferred annuity: paid sometime in the future
  • Perpetuity: payments continue forever

Annuities Formulas

• Future value: $FV = C \times \frac{[(1 + i)^n - 1]}{i}$
• Present value: $PV = C \times \frac{[1 - (1/(1 + i)^n)]}{i}$
  • C = cash flow per period
  • n = number of periods
  • i = interest rate per period

Risk and Return

• Definitions of risk:
  • Chance of loss of capital
  • Chance of loss of purchasing power
  • Variability of returns

Expected Return

• $E(R) = mean \space of \space annual \space returns$

Weighted expected return

• $E(R) = 0.20(10\%) + 0.12(40\%) + 0.10(50\%)$

Standard Deviation of Returns

• Measures the riskiness of an investment.
• Variance of returns: $\sigma^2 = \frac{\sum<em>{i=1}^{n} (X</em>i - E(R))^2}{n-1}$
• Standard deviation: $\sigma = \sqrt{\sigma^2}$

Diversification

• Reduces risk by combining assets.
• Portfolio risk is not a weighted average of individual shares' standard deviations.
• Correlation: Select assets that move in different directions to cancel out risk.
  • +1: positive correlation
  • -1: negative correlation
• Negative correlation ® Large risk reduction
• Positive correlation (+1) ® No risk reduction
• On average, the correlation coefficient for returns on two randomly selected shares would be in the range of +0.5 to +0.7.

Efficient Frontier

• Modern portfolio theory assumes risky and risk-free assets.
• Financial planners help clients decide on growth vs. fixed-interest assets based on risk tolerance.
• Formula:
• $E(R<em>p) = E(R</em>{pi}) + \sigma<em>p = \sigma</em>{pi} \times R_f$
  • $E(R_p)$ = expected return on entire portfolio
  • $E(R_{pi})$ = expected return on the risky fund
  • $\sigma_p$ = standard deviation of entire portfolio
  • $\sigma_{pi}$ standard deviation of risky fund
  • Rf = risk-free interest rate

Stand-Alone Risk

• Market risk + Diversifiable risk

Summary

• Financial planners need to understand the time value of money.
• Simple financial mathematics enable financial planners to calculate the value of different investments in different time periods.
• Investment advice needs to be based on the specific needs of the client.