Mean-variance efficient frontiers

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1. (2 points). Mean-variance efficient frontiers. There are two risky assets A and B. The means
and standard deviations of the assets’ returns are given by
Mean �” Standard Deviation �”
A 5% 10%
B 8% 15%
a. Write the equations for the mean-variance efficient frontiers when the correlation between
the two assets is -1, 0, and 1. Graph the efficient frontiers with the standard deviation on
the x axis and the mean on the y axis using your preferred graphing software. Note that
the efficient frontiers are only the regions of the feasible sets that provide the maximum
mean return for any given standard deviation. You will lose 1 point if you do not distinguish
the efficient frontier from the set of feasible mean-standard deviation combinations.
b. Consider the case where the correlation between the two assets is zero. What is the
standard deviation of asset A above which no portfolio on the mean-variance efficient
frontier includes a positive amount of asset A in the portfolio? Show your work.
2. (2 points). Consumption CAPM. Assume utility is of the quadratic form �(�) = �� − +
,
�,
and a representative investor chooses a portfolio to solve the two-period utility maximization
problem
max�(�0) + 3��”�(�6
”
)
7
“8”
�.�. �0 + 3�”�6
”
7
“86
= �0
where the terms are defined as in class lecture 11. Assume all C’s are low enough that marginal
utility is positive. Let g = (C1-C0)/C0, the growth in consumption. Let �̃
0 be the return to a
portfolio that is uncorrelated with �A.
Show that, in equilibrium, the expected return to any portfolio, �̃
B, equals the sum of the
expected return of �̃
0 plus the beta from a regression of the portfolio return on consumption
growth times some constant Z:
�[�̃
B] = �[�̃
0] + �G
B�
Where
�G
B = ���(�̃
B, �A)
���(�A)
Useful facts: For any constants d, f, and h and random variables v and w
���(��A, �O) = ����(�A, �O) ��� ���(�A + �, �O + ℎ) = ���(�A, �O)
3. (2 points). Fundamental Theorem of Asset Pricing. Using the notation from class lecture 12,
prove that there can be no arbitrage opportunities if there exists a risk-neutral probability
measure on the set of fundamental securities.

 

 

 

 

Sample Solution

 

 

 

We Do Not Understand Anything

At the littlest sizes of presence, our originations of reality are unessential. State in the event that we experienced littler and littler sizes of our bodies, we would find that in the long run we would show up at Planck length (Roper, 131). To envision the size of Planck length, think about that as a hydrogen molecule is 10 trillion Planck lengths over. At this scale, existence as we probably am aware it can never again can be comprehended.

So I don’t get that’s meaning as far as getting ourselves? All things considered, we can appropriately say that truly, we do have reality concurring certain sizes of ourselves (bigger than Planck length), however concerning our ultra-minute selves, the fundamental matter of what our identity is, our perception of presence separates (Joplin, 12).

Who might we be without existence? A few people may state we would be nothing, while others may state we would resemble virtual particles, flying all through presence—which is somewhat more than nothing, however it can’t be said to carefully exist. It would mean we exist and don’t exist all the while. This thought relates to my next point: that any inquiry we pose can be replied from numerous points of view.

The response to any question is vague when attempting to state demanding truth (Hopp, 45). Take a basic inquiry for a model: “What is your name?” My name is Nicholas David Klacsanzky as indicated by law, yet my name could be any number of names that I have appended to my character, and others have given me. Is my legitimate name my actual and just name? That is up for understanding. Also, actually, any announcement of assumed “truth” can be disentangled to show that there is another approach to take a gander at it.

There is a Zen apothegm that comes this way, “To talk is to commit an error.” This is said with the possibility that reality can’t be spoken, as truth is comprehensive and even past being—it would need to be spoken about in wording that don’t exist in language all together for the truth of reality to be seen through language (which is a Catch 22).

Along these lines, truth is an encounter. I accept this is the reason Socrates stated, “I know just of my own obliviousness,” and made the individuals at the highest point of old Greek society confounded about their fundamental ideas of their reality. We can’t comprehend reality through mental ideas: just through our unadulterated experience without the deterrent of mental movement.

Without the interference and blurring of reality by mental procedures, presence is clear. We don’t have to comprehend anything so as to know presence for what it’s worth. Truth be told, the main way we can see the truth is by quitting any pretense of attempting to comprehend and quitting any pretense of “getting” itself. At that point we can observer life in the entirety of its significant effortlessness.

References

Roper, Jake. Troubling Truth. New York: Owl Books, 2008. Print.

Joplin, Michele. Transformative Coexistence. Chicago: Bob Fugen Press, 2012. Print.

Hopp, Jason. Untruthful Truths. Seattle: Reed Bender Press, 2013. Print.

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