Max Yasunaga
Business and Management
Definition
Risk-adjusted measure of return that is used to
evaluate the performance of a portfolio.
Purpose
The idea of the ratio is to see how much additional
return an investor receives for the additional unit of
volatility compared to a risk-free asset
How
[Return on portfolio – risk free rate] / Standard Deviation of
portfolio
Step 1
Retrieve historical prices of the stocks you want to analyze
from Yahoo Finance
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Step 1
Retrieve historical prices of the stocks you want to analyze
from Yahoo Finance
Step 2
Open the file, and delete the highlighted section, leaving
only Adj Close and Date. Rename Goog instead of AdjClose.
Sort the dates so that they are ascending and not
descending.
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Step 1
Retrieve historical prices of the stocks you want to analyze
from Yahoo Finance
Step 2
Open the file, and delete the highlighted section, leaving
only Adj Close and Date. Rename Goog instead of AdjClose.
Sort the dates so that they are ascending and not
descending.
Step 3
Do the same for all stocks and place the data side by side
with GOOG.
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Step 4
Find the average expected rate of return. This can be done
by finding all the expected returns and then averaging it.
Expected return can be found by taking the difference of
the prices and dividing it by the previous price. Example:
[(B3-B2)/B2]*100%.
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Step 4
Find the average expected rate of return. This can be done
by finding all the expected returns and then averaging it.
Expected return can be found by taking the difference of
the prices and dividing it by the previous price. Example:
[(B3-B2)/B2]*100%.
Step 5
Below Average Expected Return, find Variance and Standard
Deviation. Variance is defined as the average of
the squared differences from the Mean and Standard
Deviation is the squared root of Variance.
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Step 4
Find the average expected rate of return. This can be done
by finding all the expected returns and then averaging it.
Expected return can be found by taking the difference of
the prices and dividing it by the previous price. Example:
[(B3-B2)/B2]*100%.
Step 5
Below Average Expected Return, find Variance and Standard
Deviation. Variance is defined as the average of
the squared differences from the Mean and Standard
Deviation is the squared root of Variance.
Step 6
Build a variance covariance matrix, which finds the total
variance of the portfolio
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The diagonal values (a1&a1,
a2&a2) are found by finding the
variance of GOOG and AAPL
respectively. The values (a2&a1,
a1&a2) are found by taking the
covariance of GOOG and AAPL.
Step 7
Now lets side step. To the side, do the carry out image 15
Step 8
Now find variance of the portfolio, which will be used to
find Sharpe Ratio. Explained in image 16
Image 15
Now type 0.5 and 0.5 next to a1/goog, and
a2/aapl. These are the weights. This is
where Solver will feed back how we should
appropriate our portfolio. And then next
to total, type =(highlight cell with 0.5) +
(highlight cell with other 0.5). If you are
analyzing three stocks, then you will do the
same steps we did above, except change
the numbers 0.5 & 0.5. Total should always
sum up to 1.
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(A)
(B)
Next to Var port, type
=MMULT(TRANSPOSE(…(A)highlight the two
0.5’s in step 15…),MMULT(…(B)highlight
everything in the box we made…,…repeat
(A) in here…)) Instead of pressing enter,
you hold control shift + enter, and you will
get the variance of the portfolio.
Step 7
Now lets side step. To the side, do the carry out image 15
Step 8
Now find variance of the portfolio, which will be used to
find Sharpe Ratio. Explained in image 16
Step 9
Type “Return (port)” all the way to “Sharpe Ratio” as
shown in image 17
Step 10
Find Return on Portfolio explained in image 18
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To find Return on your portfolio, take
the expected Rate of Return of stock A
for example (which you have found
earlier) and multiply the weight
distribution to that stock.
=weighted average1 * average1 +
weighted average2*average2
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Step 11
Fill in variance of the portfolio, found earlier, and Standard
deviation, which is the squared root of the variance.
Step 12
Fill in R(port) – rf. Find rf, the yield of a US treasury bond,
which we will take as 1/365 (per day).
Step 13
Fill in the Sharpe ratio, which is the [R(port)-rf] / SD(port
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Step 14
Find ultimate weighting by using Solver on excel as shown
in image 22.
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Go to tools=> solver, and click on it.
Step 14
Find ultimate weighting by using Solver on excel as shown
in image 22.
Step 15
Fill in parameters as shown in image 23.
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First step is to set the
objective. Our
objective is maximizing
sharpe ratio. So we’ll
highlight that cell.
Then we have To Max, Min, etc. In this
scenario, we want to Maximize, so we
choose Max.
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What are you changing? You’re
changing the weight you give to
the stock you’re investing in.
The amount you invest in the
stock. $L$508 is the value of 0.5
next to a1/goog. $L$509 is the
value below that. $L$510 is the
value of 1.
Click solve. And voila! Now try to make the strongest
combinations of stocks, and maximize your SHARPE RATIOS