The portfolio consists of two assets, VBTLX and VFIAX, allocated to maximize return and minimize risk. The optimal allocation was found to be 68% VBTLX and 32% VFIAX, achieving a higher Sharpe Ratio than either individual asset. This designed portfolio was then benchmarked against a single asset, AAPL, from August 2015 to August 2016. The results showed the portfolio had significantly lower monthly return volatility than AAPL and achieved a better overall return during the testing period, demonstrating the portfolio was more efficient for the given level of risk.

1. Portfolio Performance Presentation
Wharton Business and Financial Modeling Capstone:

2. • The portfolio presenting Modern Portfolio
Theory consists of two assets: VBTLX and
VFIAX.
• To design find the optimal risky portfolio:
• With the goal of maximizing return with
given risk.
• Divide investment into two (probably)
different proportion.
I. Portfolio Design

3. • We want to solve for variable (weight for VBTLX):
• and then
• To compute expected return of the portfolio:
• .
• To compute expected variance of the portfolio:
• .
• Sharpe Ratio:
I. Portfolio Design
w1
w2 = 1 − w1
E[rp] = w1 * E[r1] + w2 * E[r2] = w1 * E[r1] + (1 − w1) * E[r1]
σ2
p = w2
1 * σ2
1 + w2
2 * σ2
2 + 2w1w2Cov(r1, r2)
rp − ri
σp

4. I. Portfolio Design
Next, maximize the Sharpe Ratio of the
Portfolio to solve for w1
VBTLX VFIAX Portfolio
Mean 0.17% 1.24% 0.51%
Var 6.43533E-05 0.000896561 0.000115
STDEV 0.008106944 0.030259487 0.01071
Covariance -1.74241E-05
Correlation -0.072539492
Sharpe 0.210210745 0.409100343 0.479588
VBTLX 68%
VFIAX 32%

5. To benchmark the designed
portfolio we test the allocation
again a single asset AAPL from
August 2015 to August 2016 (not
used for training portfolio weight).
II. Portfolio Benchmark
Date Adj Close
8/3/15 110.997612
9/1/15 108.576057
10/1/15 117.632263
11/2/15 116.949501
12/1/15 104.058365
1/4/16 96.228775
2/1/16 96.104874
3/1/16 108.330437
4/1/16 93.172722
5/2/16 99.860001
6/1/16 95.599998
7/1/16 104.209999
8/1/16 106.050003

6. 8/3/15
10/1/15
12/1/15
2/1/16
4/1/16
6/1/16
-14% -7% 0% 7% 14%
$3,000,000
$3,750,000
$4,500,000
$5,250,000
$6,000,000
8/3/15
10/1/15
12/1/15
2/1/16
4/1/16
6/1/16
Portfolio Return AAPL Return
*Simulation assuming investing $5M into each.Monthly return comparison
III. Portfolio Return vs. AAPL Return

7. IV. Portfolio Summary
• The portfolio shows significantly lower volatility in monthly return.
• The portfolio gives better overall return than a single asset in the
span of the testing period.
• Even though the better return does not necessarily signify
better investment, the lower volatility and higher return shows
the portfolio is more efficient.
• The result of the case shows the Sharpe Ratio is a good
measure meant for expected return compares to risk.