Building an Efficient Frontier and Capital Market Line from Portfolio Weights
Summary
The document discusses a student’s portfolio-management exercise involving three risky assets, expected returns, standard deviations, a tangency portfolio, and a mix of that portfolio with a risk-free asset. The response focuses on clarifying how to generate portfolio points for a graph rather than solving every part of the assignment. For the risky-asset frontier, it says to calculate portfolio returns and standard deviations for multiple asset-allocation combinations; individual asset standard deviations alone are not the requested plotted series.
It distinguishes the efficient frontier, formed from risky portfolios, from the capital market line, which combines the tangency portfolio with the risk-free asset. The student is also encouraged to show the work behind a disputed calculation and not rely on an unverified automated answer. The response provides no covariance data, derivations, corrected numerical results, or complete solution, and it leaves one subproblem to the student. Its guidance is conceptual and depends on the exercise’s omitted inputs and instructions.
Key ideas
- Plotting an efficient frontier requires returns and standard deviations for portfolios with different risky-asset weights.
- The requested graph concerns portfolio risk and return, not a collection of individual-asset points.
- The efficient frontier uses risky assets, while the capital market line combines a tangency portfolio with a risk-free asset.
- When a calculated result is disputed, showing the working helps identify the source of the difference.
- The response gives conceptual guidance but does not solve the full exercise.
Tags
Full text
# Asset Management (Inverse Matrix, MVP,TP etc)
# Asset Management (Inverse Matrix, MVP,TP etc)
i just found this website and hope someone can help me. We have a midterm and we got 1 old exam but the Prof didnt want to provide the solutions and he is terrible anyway - so it kinda sucks, and i dont know if i am on the right path. we have to calculate everything with hand without excel) thanks a lot in advance.
a) using gauss jordan: i have x= 40 y=30 z=20
b) A: 0.80 B: -0.20 C:.0.40 Expected Return: 17% SD: 14.1421%
c) (0.18 0.23 0.13)
d) w* TP: A: 0.70 B: 0.093 C: 0.213 SD(TP): 15.33% SR: 1.14611
e) so from here on i struggel alot
70% TP and 30% Riskfree Expected Return:0.14264 SD: 10.731%
f) i have A: 15.21 but Chat GPT says 7.5 and i dont know wich values do i use here? The ones from 100% TP or from the 70/30 portfolio?
g) how do i calculate the SD of each Asset to plot it?
h) didnt even try yet
## Answer by KaiSqDist (score 1)
https://quant.stackexchange.com/a/77755
From what I understand of your questions, they are related to f) and g).
f) Can you list your workings for this question? ChatGPT is famously known to be unreliable. From what I understand, you subsitute everything in the first-order condition to obtain a value for $\sigma_{TP}$ correct?
g) He is not asking you to calculate the SD of individual assets to plot many efficient frontiers, he is asking you to calculate the SDs (and returns) of the portfolio based on different asset allocation combinations. For example, (A,B,C) = (30%,30%,40%) or (A,B,C) = (40%,30%,30%) until you can obtain a single frontier. The second part he asks you to plot the capital market line, it should look something like this (take note that the efficient frontier consists only of risky assets while the CML contains both risky and riskless assets):
Actually, from what I understand, you do not even have to calculate anything, just make a drawing like above.
h) Please try it on your own first.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.