- CFA Exams
- CFA Level I Exam
- Study Session 18. Portfolio Management (1)
- Reading 52. Portfolio Risk and Return: Part I
- Subject 4. Risk Aversion and Portfolio Selection

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**CFA Practice Question**

If I can borrow at the risk-free rate and use these funds to purchase portfolio X (from the previous problem), then ______

B. I will create a portfolio with less risk than X.

C. I will create a portfolio with more risk than X.

D. my new portfolio will have an expected return less than X's.

A. I will generate a rate of return equal to X's.

B. I will create a portfolio with less risk than X.

C. I will create a portfolio with more risk than X.

D. my new portfolio will have an expected return less than X's.

Correct Answer: C

The portfolio's risk is equal to the weight in X times X's standard deviation. Borrowing at the risk-free rate allows us to establish a weight in X that is greater than 100%. Therefore, the risk level will exceed that of X alone.

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**User Contributed Comments**
21

User |
Comment |
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0is4eva |
CFA program curriculum: "You either invest part of your portfolio in the risk-free asset (i.e., you lend at the RFR) and the rest in the risky asset Portfolio M, or you borrow at the riskfree rate and invest these funds in the risky asset portfolio. In either case, all the variability comes from the risky asset M portfolio. The only difference between the alternative portfolios on the CML is the magnitude of the variability, which is caused by the proportion of the risky asset portfolio in the total portfolio." |

dizzel |
I dont really get it... How come we get more than 100% in X??? I mean 100%=Risk-free Rate Investment + Portfolio X. Can someone explain this to me please? |

nike |
you can always create a portfolio that is riskier than X (or any portfolio). Every portfolio has its own risk, and they can be different. |

Khadria |
Here, its not mentioned is X is on EFFICIENT FRONTIER ! ! ! DO NOT ASSUME ! |

tonypractice |
still very unclear. a portfolio can only have a 100% weight since all the funds will be allocated to class(es). So portfolio X has a weight of 100% , where 100% of the funds are allocated to whatever class. I therefore do not understand how adding more funds would "establish a weight in X that is greater than 100%" ?? |

bdaguy |
This is an example of LEVERAGE. You're borrowing money at risk-free and using it to purchase the portfolio X which has a higher expected return but also higher risk. Your degree of leverage depends on the amount borrowed relative to the amount of your own capital used (think back to "debt/equity ratio") Example 1 - 1 year investment, no leverage: Capital invested: $100 Invest $100 in portfolio X. Portfolio X rises 10% Return on capital invested = 5% Example 2 - 1 yr investment with leverage: Capital invested: $100 Borrow $100 at 5% risk-free rate Interest due at end of year = $100 x 5%= $5 Invest $200 in portfolio X. Portfolio X rises 10% Return on capital invested=((200*10% - $5)/100) = 15% Example 3 - same as Ex.2 but with 10% portfolio loss Return on capital invested=((200*(-10%) - $5)/100) = -25% In example 2, the return is magnified with leverage is used. However, example 3, with a 10% portfolio loss creating a 25% investment loss, the risk is much higher as well. |

chamad |
Leveraging is outlined in the following Study session. Bdaguy example is good Thanks |

mariodeb |
Why is the Return on Capital Invested in bdaguy's example 1 at 5% and not 10% |

steved333 |
Simple: Leverage magnifies return. That means if your investment tanks, and some of that investment is from borrowed funds, you now owe the difference including what was lost. |

ridone |
the example by bdaguy is good but I think his return on capital figures are wrong. |

firasoweis |
no they are not wrong, they are the returns - the riskfree rate which is 5%.... in other words they are the return beyond the RFR |

DarkOblivion000 |
I still don't understand example 1. So if you contribute $100 of capital, borrow $0, the fund achieve 10% returns, then return on capital invested = ($100 x 10%) / $100 = 10% right? Why is it 5%? Yes, leverage magnifies return, but in example 1, there is NO leverage, so you should have the same return as the fund. Can someone please point out the flaw in my logic? |

jpducros |
bdaguy, you're great ! DarkOblivion000, I think you're right, there must be a typo error in bdaguy's example 1. |

gmilchev |
Thank you bdaguy. This was very helpful. |

thekobe |
take into consideration this, the sum of the invested proportions should equal 100%, but you can be short on risk free and long on risky asset, that is (long on risky asset 200%, and short on risk free -100%, so your total investment equals 100%) |

viruss |
Thinking more simply, you will incure a risk by borrowing (you owe money) and you have uncertainty on the return X (standard deviation X) > in case of financial trouble (X bankrupcy e.g.), you will still have to repay the borrowing funds while if they were yours, we owe nothing... |

johntan1979 |
Shows that some of you guys never read the notes before attempting this question. There's a great example in the notes. Sorry to say this but you ain't gonna make it if you don't read. |

jonan203 |
you have $100 and invest 50% in each investment: e(r) = .50(.12) + .50(.05) = 8.5% if you borrow $100 dollars and buy X your expected return is e(r) = .75(.12) + .25(.05) = 10.25% is 10.25% your return, no, why? because you have leveraged your portfolio. your equity is $200/$100 = 50%; however, the total weighting is still 100% (.75 + .25) the returns associated with the borrowed money is what increases your return: [($50+$100 borrowed)*(.12) + $50(.05)]/ $100 equity = 20.50% borrowing money reduces equity, yet the overall weight of the portfolio still totals 100% |

jonan203 |
btw, i didn't adjust the above example by the risk free rate. if i did, at year end your return is: [$150(.12) + $50(.05) - $100(.05)]/$100 = 15.50% |

degosan9 |
Bdaguy gives the numbers example, steved333 gives the simple answer, and if you google margin account risks it will all make sense |

pigletin |
its essentially a math problem To get higher weights for 1-x?you have to make x negative?and this translates into financial words as borrowing |