Basic Formulas

Calculating the return of a fund is essential to evaluate its performance and make informed investment decisions. Basic formulas provide an initial understanding of how a fund is performing in terms of gains or losses. Below, we explore the main formulas used by traders and financial analysts.

Simple Return

The simple return is the most basic way to measure a fund's performance. It is calculated by comparing the final value of the investment with the initial value.

Formula:

Return = ((Final Value - Initial Value) / Initial Value) * 100

For example, if you invested $10,000 in a fund and it is now worth $12,000, the return would be:

Return = (($12,000 - $10,000) / $10,000) * 100 = 20%

Annualized Return

Annualized return is useful when the investment is held for more than a year. It allows you to compare funds with different time horizons.

Formula:

Annualized Return = ((Final Value / Initial Value) ^ (1 / Number of Years)) - 1

If you invested $10,000 and after 3 years you have $13,000:

Annualized Return = (($13,000 / $10,000) ^ (1 / 3)) - 1 ≈ 8.4%

Time-Weighted Return (TWR)

TWR eliminates the impact of external cash flows, such as contributions or withdrawals, providing a more accurate measure of a fund's performance.

Formula:

TWR = (1 + r1) * (1 + r2) * ... * (1 + rn) - 1

Where r1, r2, ..., rn are the returns in each sub-period.

Money-Weighted Return (MWR)

MWR takes cash flows into account, reflecting the impact of contributions and withdrawals on performance.

Formula:

It is calculated using the Internal Rate of Return (IRR) which solves the following equation:

Σ [Cash Flow at period t / (1 + IRR) ^ t] = 0

Sharpe Ratio

The Sharpe Ratio measures risk-adjusted performance. The higher the ratio, the better the performance relative to the risk taken.

Formula:

Sharpe Ratio = (Fund Return - Risk-Free Return) / Standard Deviation of the Fund

For example, if a fund has a return of 10%, the risk-free rate is 2%, and the standard deviation is 5%:

Sharpe Ratio = (10% - 2%) / 5% = 1.6

Practical Examples

Applying formulas in real situations helps solidify understanding. Below, we explore practical examples that illustrate how to calculate the return on a fund in different scenarios.

Case 1: Single Investment with No Additional Flows

Maria invests $5,000 in an equity fund. After 2 years, her investment is worth $6,000.

Simple return calculation:

Return = (($6,000 - $5,000) / $5,000) * 100 = 20%

Annualized return:

Annualized Return = (($6,000 / $5,000) ^ (1 / 2)) - 1 ≈ 9.54%

Case 2: Investment with Additional Contributions

Carlos invests $10,000 in a fund. After a year, he adds $2,000 more. After another year, his total investment is worth $14,500.

Using Money-Weighted Return (MWR):

The IRR that solves the equation must be calculated:

-$10,000 + (-$2,000 / (1 + IRR)^1) + ($14,500 / (1 + IRR)^2) = 0

Using a financial calculator or Excel, we find that IRR ≈ 10.25%

Case 3: Comparing Funds with the Sharpe Ratio

Suppose you have two funds:

• Fund A: Return of 12%, standard deviation of 6%.

• Fund B: Return of 15%, standard deviation of 10%.
  

The risk-free rate is 3%.

Sharpe Ratio Fund A:

(12% - 3%) / 6% = 1.5

Sharpe Ratio Fund B:

(15% - 3%) / 10% = 1.2

Although Fund B has a higher return, Fund A offers better risk-adjusted performance.

Case 4: Return on International Funds

If you invest in a European fund and exchange rates affect your investment, you should consider the return in your local currency.

Example: You invest €5,000 when the exchange rate is 1 EUR = 1.2 USD. Upon selling, the fund is worth €5,500 and the exchange rate is 1 EUR = 1.1 USD.

Return in euros:

((€5,500 - €5,000) / €5,000) * 100 = 10%

Initial value in USD: €5,000 * 1.2 = $6,000

Final value in USD: €5,500 * 1.1 = $6,050

Return in USD:

(($6,050 - $6,000) / $6,000) * 100 ≈ 0.83%

The exchange rate has significantly reduced your return.

Case 5: Effect of Fees and Expenses

It's important to consider fees when calculating real returns.

Example: You invest $20,000 and achieve a gross return of 8%. However, fees and expenses amount to 1.5% annually.

Net return:

8% - 1.5% = 6.5%

Your real return is 6.5%, not the initial 8%.

Factors to Consider

Calculating the profitability of a fund is more than applying formulas; it involves analyzing various factors that can influence performance. Below, we explore the key elements that every trader should consider.

Market Volatility

Financial markets are inherently volatile. Geopolitical events, changes in monetary policies, and other variables can affect fund performance.

Advice: Stay informed about economic news and how it might impact your investments.

Investment Horizon

The time you plan to hold your investment affects expected returns. Short-term investments may be riskier but potentially more profitable.

Example: An equity fund may offer high returns in the long term but suffer short-term losses due to volatility.

Diversification

Investing in different types of funds and assets can reduce risk. Diversification can improve risk-adjusted returns.

Advice: Don’t put all your eggs in one basket. Consider a mix of fixed income, equities, and other assets.

Costs and Fees

The expenses associated with managing the fund can decrease your net returns.

Advice: Review the fund's Total Expense Ratio (TER) and consider index funds or ETFs with lower costs.

Inflation

Inflation reduces the purchasing power of your earnings. It’s important to consider real returns, adjusted for inflation.

Example: If your fund yields 5% and inflation is 2%, your real return is 3%.

Currency Risk

If you invest in funds denominated in another currency, exchange rate fluctuations can affect your returns. Consider currency hedges or invest in funds with currency risk protection.

Fund Manager Performance

The skill and experience of the manager can influence performance. A good track record can be indicative of future results, though it’s not guaranteed.

Fiscal Policy

Taxes can impact net returns. Know the tax implications of your investments. In some countries, investment funds have tax advantages that can improve your net returns.

Conclusion

Calculating a fund’s profitability is a multifaceted process that goes beyond mathematics. As Benjamin Graham, the father of value investing, once said: "The main cause of poor investment results is erratic and undisciplined behavior." Consider all these factors and maintain a well-informed strategy to maximize your returns.