1st statement: If i borrow money from a bank for 1 year at 5% and then invest in a risk-free asset that has an expected return of 6% over the same year then this is an arbitrage opportunity?????2nd statement:The risk-free rate is 1.5%. There exists a pharmaceutical share that has current price of ?1 and an expected return of 80%. There is an arbitrage opportunity?Could someone help me with this? Because im really comfused about arbitrage opportunity! ! !Thank you

1) If no additional costs are occurred and a "risk free" asset exists then yes arb.2) No, arb = risk free. Not = expected to make money.Usually when asked on a arb for a test you should be able to get a profit right from the get go like in 1.

Could you please explain to me in a more analytical way why the second statement isn't an arbitrage?Thank you

QuoteOriginally posted by: trekstorCould you please explain to me in a more analytical way why the second statement isn't an arbitrage?Thank youin the first case, the outcome is bounded.. you borrow at 1.5% from a bank and lend to the government (of the country where the bank is) at 5%. you stand to make 3.5%.in the second case you buy the stock with a vol 80% - the outcome over any time is not bounded. the stock could go up but it could also fall (hence the vol of 80%)

QuoteOriginally posted by: trekstorCould you please explain to me in a more analytical way why the second statement isn't an arbitrage?Thank youIt's not risk free. You borrow at 1.5% Buy at $1 expect 80% increase but in reality it winds up going to -100% return instantly after buying ergo net loss, you have a value less stock and owe the bank 1.5%.

The test for arbitrage is that at some future point in time you will have a gain for all possible states of the world at that point in time. If there is a chance of a loss (no matter how remote the possibility or small the magnitude) it is not a true arbitrage.Regarding #1, if something is risk free there is no need to discuss expectations -- risk free implies everything is deterministic, nothing is stochastic/random/unknown.Regarding #2, you have an expected return of 80%, but a possible return of something less than 1.5%. So in this case there is no arbitrage, but you have a relative value opportunity.

thank you very much all of you