## Vanguard Rate of Return?

### Vanguard Rate of Return?

Is the Vanguard rate of return under "personal performance" an average annual rate of return, or something else?

### Re: Vanguard Rate of Return?

Things labelled as personal return are usually an internal rate of return or IRR, which is an average that takes into account contributions and withdrawals. That is why it is personal as the result would apply only to the specific details of the account. The result is usually annualized. But IRR is the best measure to use to understand how well one's actual investments are doing.

Also of interest can be time weighted return. This can be compared to compound annual growth rate (CAGR) of an investment without contributions or withdrawals. Also of note is all of these are compound averages and not arithmetic averages of returns over time. Also CAGR is the geometric average of gain factors (1+return) and not the geometric average of the actual returns. The arithmetic mean of returns in a set of time periods is used to estimate the mean of the return distribution, also called the expected return. There can also be a discussion of a generalized concept of mean including arithmetic, geometric, harmonic, etc.

The general concept of a mean is a value that can replace all instances of a set of values in a function and produce the same result as before. Many means can also be reduced to only an arithmetic mean by first applying a transformation of variables, taking the arithmetic mean, and then applying the inverse transformation. For example the CAGR is computed using the following transformations applied to returns in %: divide by 100/add 1/take the logarithm --- take the arithmetic average --- exponentiate the result/subtract 1/multiply by 100.

IRR:

https://www.investopedia.com/terms/i/irr.asp

Time Weighted:

https://www.investopedia.com/terms/t/ti ... of%20money.

CAGR: https://www.investopedia.com/terms/c/ca ... %20rate%20(CAGR,year%20of%20the%20investment%27s%20lifespan.

Geometric Mean:

https://en.wikipedia.org/wiki/Geometric_mean

Arithmetic Mean:

https://en.wikipedia.org/wiki/Arithmetic_mean

Generalized Mean:

https://en.wikipedia.org/wiki/Generalized_mean

Also of interest can be time weighted return. This can be compared to compound annual growth rate (CAGR) of an investment without contributions or withdrawals. Also of note is all of these are compound averages and not arithmetic averages of returns over time. Also CAGR is the geometric average of gain factors (1+return) and not the geometric average of the actual returns. The arithmetic mean of returns in a set of time periods is used to estimate the mean of the return distribution, also called the expected return. There can also be a discussion of a generalized concept of mean including arithmetic, geometric, harmonic, etc.

The general concept of a mean is a value that can replace all instances of a set of values in a function and produce the same result as before. Many means can also be reduced to only an arithmetic mean by first applying a transformation of variables, taking the arithmetic mean, and then applying the inverse transformation. For example the CAGR is computed using the following transformations applied to returns in %: divide by 100/add 1/take the logarithm --- take the arithmetic average --- exponentiate the result/subtract 1/multiply by 100.

IRR:

https://www.investopedia.com/terms/i/irr.asp

Time Weighted:

https://www.investopedia.com/terms/t/ti ... of%20money.

CAGR: https://www.investopedia.com/terms/c/ca ... %20rate%20(CAGR,year%20of%20the%20investment%27s%20lifespan.

Geometric Mean:

https://en.wikipedia.org/wiki/Geometric_mean

Arithmetic Mean:

https://en.wikipedia.org/wiki/Arithmetic_mean

Generalized Mean:

https://en.wikipedia.org/wiki/Generalized_mean

### Re: Vanguard Rate of Return?

Only you dbr could give such a detailed and complete answer.dbr wrote: ↑Fri Jul 31, 2020 8:16 amThings labelled as personal return are usually an internal rate of return or IRR, which is an average that takes into account contributions and withdrawals. That is why it is personal as the result would apply only to the specific details of the account. The result is usually annualized. But IRR is the best measure to use to understand how well one's actual investments are doing.

Also of interest can be time weighted return. This can be compared to compound annual growth rate (CAGR) of an investment without contributions or withdrawals. Also of note is all of these are compound averages and not arithmetic averages of returns over time. Also CAGR is the geometric average of gain factors (1+return) and not the geometric average of the actual returns. The arithmetic mean of returns in a set of time periods is used to estimate the mean of the return distribution, also called the expected return. There can also be a discussion of a generalized concept of mean including arithmetic, geometric, harmonic, etc.

The general concept of a mean is a value that can replace all instances of a set of values in a function and produce the same result as before. Many means can also be reduced to only an arithmetic mean by first applying a transformation of variables, taking the arithmetic mean, and then applying the inverse transformation. For example the CAGR is computed using the following transformations applied to returns in %: divide by 100/add 1/take the logarithm --- take the arithmetic average --- exponentiate the result/subtract 1/multiply by 100.

IRR:

https://www.investopedia.com/terms/i/irr.asp

Time Weighted:

https://www.investopedia.com/terms/t/ti ... of%20money.

CAGR: https://www.investopedia.com/terms/c/ca ... %20rate%20(CAGR,year%20of%20the%20investment%27s%20lifespan.

Geometric Mean:

https://en.wikipedia.org/wiki/Geometric_mean

Arithmetic Mean:

https://en.wikipedia.org/wiki/Arithmetic_mean

Generalized Mean:

https://en.wikipedia.org/wiki/Generalized_mean

+1

The market is the most efficient mechanism anywhere in the world for transferring wealth from impatient people to patient people.” |
— Warren Buffett

### Re: Vanguard Rate of Return?

Thank you for your thoughtful and detailed answer. Helps a lot, and gives me lots more to learn. Greatly appreciated.dbr wrote: ↑Fri Jul 31, 2020 8:16 amThings labelled as personal return are usually an internal rate of return or IRR, which is an average that takes into account contributions and withdrawals. That is why it is personal as the result would apply only to the specific details of the account. The result is usually annualized. But IRR is the best measure to use to understand how well one's actual investments are doing.

Also of interest can be time weighted return. This can be compared to compound annual growth rate (CAGR) of an investment without contributions or withdrawals. Also of note is all of these are compound averages and not arithmetic averages of returns over time. Also CAGR is the geometric average of gain factors (1+return) and not the geometric average of the actual returns. The arithmetic mean of returns in a set of time periods is used to estimate the mean of the return distribution, also called the expected return. There can also be a discussion of a generalized concept of mean including arithmetic, geometric, harmonic, etc.

The general concept of a mean is a value that can replace all instances of a set of values in a function and produce the same result as before. Many means can also be reduced to only an arithmetic mean by first applying a transformation of variables, taking the arithmetic mean, and then applying the inverse transformation. For example the CAGR is computed using the following transformations applied to returns in %: divide by 100/add 1/take the logarithm --- take the arithmetic average --- exponentiate the result/subtract 1/multiply by 100.

IRR:

https://www.investopedia.com/terms/i/irr.asp

Time Weighted:

https://www.investopedia.com/terms/t/ti ... of%20money.

CAGR: https://www.investopedia.com/terms/c/ca ... %20rate%20(CAGR,year%20of%20the%20investment%27s%20lifespan.

Geometric Mean:

https://en.wikipedia.org/wiki/Geometric_mean

Arithmetic Mean:

https://en.wikipedia.org/wiki/Arithmetic_mean

Generalized Mean:

https://en.wikipedia.org/wiki/Generalized_mean

### Re: Vanguard Rate of Return?

Here’s what Vanguard says about your personal rate of return:

Calculation method. Personal performance uses a formula called internal rate of return (IRR), which is a dollar-weighted return. IRR takes into account new money coming into your investment, as well as how long that money has been held. Don't confuse your personal rate of return with those posted for funds and indexes. The returns presented in these instances use a time-weighted calculation, which does not take cash flow into consideration.

https://personal.vanguard.com/us/conten ... ontent.jsp

- patrick013
**Posts:**2950**Joined:**Mon Jul 13, 2015 7:49 pm

### Re: Vanguard Rate of Return?

I think it's common to see an average or mean return for 5 or 10 years.

Also a compound return which includes reinvestment of dividends and

calcs what the return is with compounding for 5 or 10 years with the

starting and ending balance.

IRR, or whatever term is common, would be a compounded return with

regard for contributions and withdrawals. It can be an all-inclusive

discounted return where the present value of the cash flows leads

to the rate of return calculated. You would obviously get a better

IRR if stocks are withdrawn when stocks are up and bonds are withdrawn

when bonds are up.

Also a compound return which includes reinvestment of dividends and

calcs what the return is with compounding for 5 or 10 years with the

starting and ending balance.

IRR, or whatever term is common, would be a compounded return with

regard for contributions and withdrawals. It can be an all-inclusive

discounted return where the present value of the cash flows leads

to the rate of return calculated. You would obviously get a better

IRR if stocks are withdrawn when stocks are up and bonds are withdrawn

when bonds are up.

age in bonds, buy-and-hold, 10 year business cycle