100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Summary Portfolio Theory R147,86   Add to cart

Summary

Summary Portfolio Theory

 23 views  1 purchase
  • Course
  • Institution
  • Book

All the lecture notes by the presented graphs etc in the lectures -by Auke Plantinga

Preview 4 out of 77  pages

  • Yes
  • March 15, 2021
  • 77
  • 2020/2021
  • Summary
avatar-seller
Lecture 1 – Portfolio theory

Portfolio theory is designed by Harry Markowitz

Utility analysis
Standard neo-classical approach for facilitating decision making under risk.
The assumption is that the investor is rational > to make sure that rationality is
enforced with the utility model: six axioms
1. People have preferences
2. Peoples preferences are transitive: A over B, B over C -> A over C
3. Investment opportunities with equal expected utility are equally
desirable.
4. Utility can be used with risky decisions
5. If we have two ranked risky investment alternatives, adding a third one
that is unrelated (irrelevant) to the first two will not affect our ranking
6. People make risky decisions by maximizing their expected utility.

Which portfolio to take? A or B?
The difference between A and B depends on your preferences towards risk.
These preferences are modelled as an utility function (e.g. iso-utility curve).

Maximizing expected utility
We like to optimize the expected utility of wealth

--

Where n are the possible outcomes (scenarios), pi is the probability of the
scenario, and wi is the wealth acquired in that particular scenario

 The shape of the utility function determines risk aversion.




1

,Example: soccer scores

In the past, the following was used in counting soccer scores in a tournament.

Risk attitudes

 The first team plays a risky strategy involving an offensive playing style
while the second team plays a conservative strategy involving a
defensive playing style
 Public didn’t like too many tie’s so decided to change the wins to 3
points instead of 2: people like risk.

Intermediate conclusion:
 The weighting scheme can be adjusted to accommodate risk preference
 In utility theory, the risk preferences are implemented by choosing a
utility function
 Risk aversion/preference can be illustrated via 2 ways:
o Shape of function (exponential vs. quadratic)
o Parameters used (2x^3 or 3x^2)




2

,Utility of wealth and returns

 Ultimately, we are interested in the utility of wealth (as opposed to the
utility of returns because in the end, the wealth (money amount able to
spend), determines the purchasing power and so utility of consumption).
 However, for reasons of convenience, we transform wealth into one-
period returns without affecting the preference order.

--
Initial wealth level where r means the return

 We prefer returns over wealth for many reasons, including comparability
between individuals with different wealth, statistical properties in time
series analysis (stationary)
 Wealth = explosive process, you can admit when you plot the numbers
 Returns as % = approximately with constant deviation

Example expected utility of returns
Since all three assets have the same expected return, preference orderings
must arise from differences in risk attitude.




3

, Properties of utility functions
1. Non-satiation: economic subjects prefer more over less. This can be seen
through the first derivative: positive
a. First derivative >0 ---
2. Risk preference: second derivative
a. Second derivative <0: risk aversion (concave) = negative but
doesn’t mean that you don’t want to take risk, but want to be
awarded for it
b. Second derivative = 0: risk -neutrality
c. Second derivative >0: risk-loving / preference (convex)

Another way of looking at risk aversion is the fair game concept
 A fair game is essentially a lottery with an expected value of zero. The
investment equals the outcome, so the expected value is zero.

Example of a fair gamble
An investor with initial wealth of 1000 considers a lottery with 50% chance of
winning 300 and 50% chance of losing 300. Participating in the lottery does not
require an investment.

If the expected utility after playing the game exceeds the expected utility
before playing the game, then the investor should take the lottery.

--

The investor would reject this lottery




4

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying this summary from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller demipoppe81. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy this summary for R147,86. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

85443 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy summaries for 14 years now

Start selling
R147,86  1x  sold
  • (0)
  Buy now