Arbitrage - I got the answer but could I prove with math from dat?

[archived_user]

The question is below. I get the answer given the concept of arbitrage, but how would I prove this out mathematically from the data easily?
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An analyst determines that a portfolio with a 35% weight in Investment P and a 65% weight in Investment Q will have a standard deviation of returns equal to zero.

• Investment P has an expected return of 8%.
• Investment Q has a standard deviation of returns of 7.1% and a covariance with the market of 0.0029.
• The risk-free rate is 5% and the market risk premium is 7%.

If no arbitrage opportunities are available, the expected rate of return on the combined portfolio is closest to: ANSWER: 5%

 

[archived_user]

By definition, no arbitrage opportunities means that a risk-free portfolio earns the risk-free rate.
There is no mathematical proof; it’s simply the definition of arbitrage.

 

[archived_user]

OK thank you, I will put the pen and paper down.

 

[archived_user]

Sounds like a plan.
You’re quite welcome.

 

[archived_user]

Hey, can you please show your workings? Thanks!

 

[archived_user]

Wutang wrote: Hey, can you please show your workings? Thanks!

There are no workings. That’s the point.