How to Solve for Money Weighted Return Without Calculator
The understanding of investment returns brings about proficient portfolio management. A very significant measure is Money Weighted Return, or in common parlance, Internal Rate of Return. This article provides guidelines about How to solve for money weighted return without calculator concept and step-by-step approach without the calculator to solve MWR. You will understand how to determine MWR manually, thereby guiding your investment decisions at the end.
What is Money Weighted Return?
Money Weighted Return is an accounting for cash inflows and outflows in terms of both time and the dollar amount of the inflow/outflow. Unlike TWR, which views performance as purely the return on the investment, ignoring inflows and outflows, MWR actually gives you a more realistic view of your actual return based on your contribution or withdrawal dates.
Important Features of Money Weighted Return:
– The Time Value of Cash Flows: It captures in the book when cash flows are being put into or withdrawn from an investment.
– **Real Investor Experience**: It replicates the actual returns earned by the investor.
– **Sophisticated Calculation**: Although MWR is simple to compute with a computer or financial calculator, how to do this calculation by hand also needs to be learned.
Money Weighted Return Significance
Calculating MWR helps the investors evaluate how their investment strategies performed. It helps them know whether cash flow timing has impacted their total return negatively or positively. Knowing MWR allows the investor to adjust and do better in the future.
How to Calculate Money Weighted Return Without a Calculator
Step 1: Identify Your Cash Flow Data
Gather all cash flow information about your investment in a specified period of time. You will need:
– Opening investment**: initial amount invested.
– Follow-up cash flow**: additional investitures in the course of the investment period and withdrawals at the same period of time.
– Closing value**: final amount of the investment.
Example**
– Opening investment: $1,000
– Subsequent investment: $500 after 1 year
– Closing value: $1,800 after 2 years
### Step 2: Determine the Time Periods
Determine the appropriate time periods for the associated cash flows. This will allow you to assign a time value to each investment.
– **Initial Investment**: Year 0 (time = 0)
– **Additional Investment**: Year 1 (time = 1)
– **Ending Value**: Year 2 (time = 2)
### Step 3: Derive the Cash Flow Formula
MWR can be solved by using the so-called equation that combines inflows and outflows of cash at present value. The equation looks like this:
\ }
0 = C_0 + \\\\frac{C_1}{(1 + r)} + \\\\frac{C_2}{(1 + r)^2}
\ }
Where:
– \\\\( C_0 \\\\) = initial cash flow (negative for outflows)
– \\\\( C_1 \\\\) = cash flow at year 1 (negative for outflows)
– \\\\( C_2 \\\\) = ending value (positive for inflows)
– \\( r \\) = MWR (the rate you’re solving for)
### Step 4: Plug in Your Values
Using the test values:
– \\( C_0 = -1000 \\
– \\( C_1 = -500 \\
– \\( C_2 = 1800 \\
The equation becomes
\\[
0 = -1000 – \\frac{500}{(1 + r)} + \\frac{1800}{(1 + r)^2}
\\
### Step 5: Rearrange the Equation
To make it easier to solve for \\\\( r \\\\), multiply through by \\\\((1 + r)^2\\\\) to eliminate the fractions:
\\\\[\\
0 = -1000(1 + r)^2 – 500(1 + r) + 1800\\
\\\\]
### Step 6: Expand and Simplify
Expand the equation:
\\\\[\\
0 = -1000(1 + 2r + r^2) – 500(1 + r) + 1800\\
\\\\]
This gives:
\\\\[\\
0 = -1000 – 2000r – 1000r^2 – 500 – 500r + 1800\\
\\\\]
Now combine like terms:
\\\\[
0 = -1000r^2 – 2500r – 700
]
Step 7: Solve the Quadratic Equation
Now, take this equation and put it into the standard quadratic format:
[
1000r^2 + 2500r + 700 = 0
]
You can now solve this quadratic with the quadratic formula:
[
r =
−b ± sqrt(b2 − 4ac)
2a
]
Where:
– a = 1000
– b = 2500
– c = 700
Now plug in those values:
[
r =
−2500 ± sqrt((2500)2 − 4(1000)(700))
2(1000)
]
END
Step 8: Find the Roots
1. Calculate the discriminant:
– \\\\( 2500^2 – 4 \\\\times 1000 \\\\times 700 \\\\)
– This will be the number to take as the argument of the square root.
2. Solve for \\\\( r \\) by the Quadratic Formula.
Step 9: Discuss
The value you find for \\\\( r \\\\) will be the Money Weighted Return. And of course, you should express this value as a percentage by multiplying it by 100.
Conclusion
Calculating money-weighted return on a hand may seem complicated at first glance, but breakdown into simple steps makes it feasible. As a result of going through this step-by-step guide, one would easily be able to determine his investment performance without the use of a calculator. MWR knowledge will arm one with the capacity to make better investment decisions and align financial strategies with their desired goals.
With this as your base knowledge, you could plunge boldly into your investments, always optimizing the returns from real cash flow experiences. Happy investing!
