hi, could someone confirm some doubts for me please?

[Asset allocation]

[1]if the expected return on tangency portfolio < required return

  • …and borrowing is allowed : we could leverage Tangency Portfolio,moving along the CAL eastwards from the TP,increasing risk and return but maintaing the Sharpe ratio.
  • …and borrowing is not allowed : we could use the corner portfolio theorem,combining the CP with the return that is greater than the required return with an adjacent CP that brackets the return requirement

[2]if the expected return on tangency portfolio > required return

  • …and borrowing/lending is not allowed / or otherwise we are directed to only invest in one of the listed CPs : we would invest in the TP.
  • …and borrowing/lending is allowed : we would combine the rf with the TP to move westwards of the TP on the CAL,thus lowering risk,return,while maintaining the Sharpe ratio of the TP.
  • …theoretically : we could combine the TP with an adjacent CP,but this is sub optimal because we would be lowering the Sharpe Ratio.

Also, any movements along the CAL would involve the same Sharpe ratio because the ratio is the slope of the CAL.

is this ok?

[Callable/ putable structures/ others]

1.interest decrease/volatility increases -> callable and putable underperforms bullet.

2.interest increase/volatility decrease -> callable and putable overperforms bullet.

3.More issuance of investment grade coprporate bonds -> price increases

4.Positive relationship between liquidity and prices.

5.interest rates increase ->Buy short DUR bond/sell long DUR bond

6.yield spread for sector increases -> Select shorter DUR bonds

7.Companies will issue more investment grade bonds when credit spreads are narrowing.

could someone explain point 5 please? i understand why we sell long DUR bonds when interest rate increases (because we want to get rid of those bonds that will decline in price drastically) But why would we want to buy short DUR bonds?


1.negative skewness->underestimates volatility->underestimates VaR.

2.leptokurtosis -> overestimates return -> understates VaR.

Thanks guys