Other
Investment Analysis formulas
- Course
- Institution
All the formulas for Investment Analysis course for master students finance at Tilburg University.
[Show more]
1 review
By: spwe95 • 7 year ago
Seller
FollowLVermunt
Reviews received
Content preview
FORMULAS IAPart 1
5% probability that portfolio will fall in value by more than VaR over one year period.
𝑉𝑎𝑅$%%&$' = 𝑊+ 1.64𝜎$%%&$' − 𝜇$%%&$'
𝑉𝑎𝑅$%%&$' = 𝑊+ 12 ×1.64𝜎56%+7'8 − 12 ×𝜇56%+7'8
GUISE: 𝑥:.;: = 0.3125𝑥:.:; + 0.4375𝑥:.:A + 0.2500𝑥:.;: 𝑥B = 𝑊: ×𝑒𝑥𝑝 𝐻𝜇 + 𝑧B 𝜎 𝐻
𝑟H = 𝑟I + 𝛽H 𝑟5 − 𝑟I
𝜎K = 𝑦𝜎M
𝐶𝑜𝑣 𝑟H , 𝑟5
𝛽H =
𝑉𝑎𝑟 𝑟5
U
𝜌ST = VW 𝜎ST = 𝜌ST × 𝜎S × 𝜎T
UV UW
𝑟K = 𝑤S 𝑟S + 𝑤T 𝑟T
Y
𝜎ST = 𝑤SY 𝜎SY + 𝑤TY 𝜎TY + 2𝑤S 𝑤T 𝜎ST
1
𝑈 𝐶 = 𝐸 𝑟K − 𝐴 ×𝑉𝑎𝑟 𝑟K
2
Matrix notation
𝑤; 1
𝑤= ⋮ 𝜄= ⋮ weight of risk-free asset 𝑤`a = 1 − b
Hc; 𝑤H = 1 − 𝑤 d𝜄
𝑤^ 1
𝐸 𝑟; − 𝑟I
Return of combination portfolio: 𝑟K = 𝑟I + 𝑤 d 𝑟Me where 𝑤 d = 𝑤; … 𝑤^ and 𝑟Me = ⋮
𝐸 𝑟^ − 𝑟I
𝐸 𝑟; − 𝑟I
d e ⋮ e
Expected return: 𝐸 𝑟K = 𝑟I + 𝑤 𝜇 where 𝜇 =
𝐸 𝑟^ − 𝑟I
𝜎;Y ⋯ 𝜎;b 𝑤;
Variance: 𝑉𝑎𝑟 𝑟K = 𝑤 d
𝑤 = 𝑤; … 𝑤^ ⋮ ⋱ ⋮ ⋮
𝜎b; ⋯ 𝜎bY 𝑤^
;
Find optimal complete portfolio weights (maximize U): 𝑈 𝐶 = 𝐸 𝑟K − 𝐴 ×𝑉𝑎𝑟 𝑟K
Y
;
= 𝑟I + 𝑤 d 𝜇 e − 𝐴 ×𝑤 d 𝑤
Y
e
𝜇 − 𝐴Σ𝑤 = 0
𝐴Σ𝑤 = 𝜇 e
𝑤 ∗ = 𝐴k; Σ k; 𝜇 e
, Optimal portfolio with exogenous risk
𝑟K = 𝑟I + 𝑤 d 𝑟Me + 𝑞 × 𝑟m
𝐸 𝑟K = 𝑟I + 𝑤 d 𝜇 e + 𝑞𝜇m
𝑉𝑎𝑟 𝑟K = 𝑤 d Σ𝑤 + 𝑞 Y 𝜎mY + 2𝑤 d 𝜎`n 𝑞
𝑤 ∗ = 𝐴k; Σ k; 𝜇 e − 𝑞Σ k; 𝜎`n
Part 2
Equity
𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒
𝑇𝑜𝑏𝑖𝑛𝑠 𝑞 =
𝑟𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑎𝑠𝑠𝑒𝑡𝑠
T S• € T •• k •‚
Expected stock return: 𝐸 𝑟 = 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑌𝑖𝑒𝑙𝑑 + 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐺𝑎𝑖𝑛 𝑌𝑖𝑒𝑙𝑑 =
•ƒ
T S• € T ••
Intrinsic value: 𝑉: =
;€^
1. DDM:
S• S„ S… € •…
a. Finite horizon: 𝑉: = + +⋯+
;€^ ;€^ „ ;€^ …
‡ S
b. Infinite horizon: 𝑉6 = +c; † †
;€^
c. Dividend growth:
i. Constant dividend growth model: 𝑔 = 𝑅𝑂𝐸 × 𝑏
1. 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠+€; = 𝐵𝑜𝑜𝑘𝑣𝑎𝑙𝑢𝑒 +€; ×𝑅𝑂𝐸
2. 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠+€; = 𝐵𝑜𝑜𝑘𝑣𝑎𝑙𝑢𝑒+ + 𝐵𝑜𝑜𝑘𝑣𝑎𝑙𝑢𝑒+ ×𝑏 ×𝑅𝑂𝐸 ×𝑅𝑂𝐸
a. 𝑅𝑒𝑡𝑎𝑖𝑛𝑒𝑑 = 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 ×𝑏
b. 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑝𝑎𝑦𝑒𝑑 𝑜𝑢𝑡 = 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 × 1 − 𝑏
Ž ;€ Œ• † S• ;€ Œ„
ii. Multistage growth models: 𝑃: = 𝐷: +c; ;€^ † + ^k Œ ;€^ •
„
S• ;€Œ
1. Determine price at end with 𝑃: = , add and discount
^kŒ
2. P/E ratios and growth opportunities:
𝑃𝑟𝑖𝑐𝑒 = 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐴𝑠𝑠𝑒𝑡𝑠 𝑖𝑛 𝑃𝑙𝑎𝑐𝑒 + 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐺𝑟𝑜𝑤𝑡ℎ 𝑂𝑝𝑝𝑜𝑟𝑡𝑢𝑛𝑖𝑡𝑖𝑒𝑠
•ƒ ; ••‘’
a. = 1+ T
T• ^ ^
T•
i. If PVGO=0, 𝑃: =
^
S• T•
ii. 𝑃𝑉𝐺𝑂 = 𝑃𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 − 𝑁𝑜𝑔𝑟𝑜𝑤𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 = −
^kΠ^
•ƒ ;k”
b. =
T• ^k•’T×”
• ;k”
c. =
T ^kŒ
Empirical Evidence CAPM
1. Estimating betas
a. Theory: 𝐸 𝑟H = 𝑟I + 𝛽– 𝐸 𝑟— − 𝑟I
b. Data: 𝑹𝒊𝒕 − 𝑹𝒇𝒕 = 𝜶𝒊 + 𝜷𝒊 𝑹𝒎𝒕 − 𝑹𝒇𝒕 + 𝜺𝒊𝒕 estimate using time series regressions
2. Regressing returns on betas (average returns on constant β, for every month on time-varying β)
a. Theory: 𝐸 𝑅H+ − 𝑅I+ = 𝜆+ 𝛽+ cross-sectional return-beta relationship
b. Data: 𝑹𝒊𝒕 − 𝑹𝒇𝒕 = 𝝀𝟎𝒕 + 𝝀𝟏𝒕 𝜷𝒕 + 𝜺𝒊𝒕 estimating SML
The benefits of buying summaries with Stuvia:
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
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
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 these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller LVermunt. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.25. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
64438 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now