Portfolio risk and return - Question

[S2000magician]

@MrSmart

@S2000magician

But correlation of returns doesn’t track value.

I think you misunderstand how correlation works. Look at the example I posted above, for two stocks that were chosen essentially at random.

How is return calculated in this example, capital gain+income on the stock or net income on the IS?

Price appreciation plus dividends: use the adjusted closing price column.

There’s no getting around it: correlation of returns and correlation of prices have nothing to do with each other.

[MrSmart]

@S2000magician

@MrSmart

@S2000magician

But correlation of returns doesn’t track value.

I think you misunderstand how correlation works. Look at the example I posted above, for two stocks that were chosen essentially at random.

How is return calculated in this example, capital gain+income on the stock or net income on the IS?

Price appreciation plus dividends: use the adjusted closing price column.

There’s no getting around it: correlation of returns and correlation of prices have nothing to do with each other.

That’s a bold statement IMO. Using that logic, two assets with (almost) perfectly correlated returns should have random correlations of their price movements?

[S2000magician]

@MrSmart

@S2000magician

@MrSmart

@S2000magician

But correlation of returns doesn’t track value.

I think you misunderstand how correlation works. Look at the example I posted above, for two stocks that were chosen essentially at random.

How is return calculated in this example, capital gain+income on the stock or net income on the IS?

Price appreciation plus dividends: use the adjusted closing price column.

There’s no getting around it: correlation of returns and correlation of prices have nothing to do with each other.

That’s a bold statement IMO.

I’m accustomed to making bold statements.

@MrSmart

Using that logic, two assets with (almost) perfectly correlated returns should have random correlations of their price movements?

“Random” seems inappropriate here; the correlation of price movement isn’t random.

A better statement, I believe, is that merely knowing the correlation of their returns isn’t sufficient to make any statement about their correlation of prices. The two quantities are, essentially, statistically independent.

[MrSmart]

@S2000magician

@MrSmart

@S2000magician

@MrSmart

@S2000magician

But correlation of returns doesn’t track value.

I think you misunderstand how correlation works. Look at the example I posted above, for two stocks that were chosen essentially at random.

How is return calculated in this example, capital gain+income on the stock or net income on the IS?

Price appreciation plus dividends: use the adjusted closing price column.

There’s no getting around it: correlation of returns and correlation of prices have nothing to do with each other.

That’s a bold statement IMO.

I’m accustomed to making bold statements.

@MrSmart

Using that logic, two assets with (almost) perfectly correlated returns should have random correlations of their price movements?

“Random” seems inappropriate here; the correlation of price movement isn’t random.

A better statement, I believe, is that merely knowing the correlation of their returns isn’t sufficient to make any statement about their correlation of prices. The two quantities are, essentially, statistically independent.

Can’t wrap my head around it.

If the price appreciation of two assets are positively and strongly correlated, then their price has to exhbit the same pattern because price appreciation cannot happen without their respective prices moving in the same direction, how are they independent? Unless either the dividends in both assets are distorting the statistic wildly, or the volatility for one (or both) of them is extremely high. But that shouldn’t be the case for two stalwart stocks.

[S2000magician]

@MrSmart

@S2000magician

@MrSmart

@S2000magician

@MrSmart

@S2000magician

But correlation of returns doesn’t track value.

I think you misunderstand how correlation works. Look at the example I posted above, for two stocks that were chosen essentially at random.

How is return calculated in this example, capital gain+income on the stock or net income on the IS?

Price appreciation plus dividends: use the adjusted closing price column.

There’s no getting around it: correlation of returns and correlation of prices have nothing to do with each other.

That’s a bold statement IMO.

I’m accustomed to making bold statements.

@MrSmart

Using that logic, two assets with (almost) perfectly correlated returns should have random correlations of their price movements?

“Random” seems inappropriate here; the correlation of price movement isn’t random.

A better statement, I believe, is that merely knowing the correlation of their returns isn’t sufficient to make any statement about their correlation of prices. The two quantities are, essentially, statistically independent.

Can’t wrap my head around it.

If the price appreciation of two assets are positively and strongly correlated, then their price has to exhbit the same pattern because price appreciation cannot happen without their respective prices moving in the same direction, how are they independent?

Asset A has returns of 1%, 2%, 3%, 4%, 5%: its price is increasing.

Asset B has returns of -5%, -4%, -3%, -2%, -1%: its price is decreasing.

Correlation of Asset A’s returns and Asset B’s returns: +1.0.

Correlation of Asset A’s prices and Asset B’s prices: -0.87.

The key information that is missing from the correlation of returns is the value of the mean return for each asset. That’s crucial information for determining the correlation of prices.