{"id":8465,"date":"2026-02-14T16:10:47","date_gmt":"2026-02-14T12:10:47","guid":{"rendered":"https:\/\/eoninvestment.com\/?p=8465"},"modified":"2026-04-10T22:56:15","modified_gmt":"2026-04-10T18:56:15","slug":"value-at-risk","status":"publish","type":"post","link":"https:\/\/eoninvestment.com\/ka\/2026\/02\/14\/value-at-risk\/","title":{"rendered":"\u10e4\u10d0\u10e1\u10d4\u10e3\u10da\u10dd\u10d1\u10d0 \u10e0\u10d8\u10e1\u10d9\u10d8\u10e1 \u10e5\u10d5\u10d4\u10e8 (VaR)<\/span>"},"content":{"rendered":"

While the Greek letters view portfolio risk from multiple angles and generate numerous risk measures, the VaR (Value at Risk)<\/strong> metric is an attempt to express portfolio risk in a single parameter. It answers a question roughly like this:<\/p>\n\n\n\n

\n

With 99% confidence, what is the minimum loss the portfolio could incur over the next 10 days?<\/p>\n<\/blockquote>\n\n\n\n

If we assume that the portfolio\u2019s expected return is normally distributed, there is a threshold on the left tail of the distribution beyond which the worst X% of outcomes occur. VaR shows the loss at precisely that threshold.<\/p>\n\n\n\n

However, because events beyond that threshold may unfold differently across portfolios, another parameter was introduced: Expected Shortfall (ES)<\/strong>. Put simply, if VaR tells us how bad things could get, ES tells us the expected loss if things do get that bad.<\/p>\n\n\n\n

In the diagrams below, two portfolios are shown with the same VaR but different expected losses (one has a fatter tail).<\/p>\n\n\n\n

\"\"\/ \"\"\/<\/p>\n\n\n\n

\n\n\n\n

Historical Simulation of Risk Measures<\/h3>\n\n\n\n

Risk measures can be derived either through historical analysis or through modeling. Below is an example of the historical simulation approach:<\/p>\n\n\n\n

Let\u2019s assume we have a portfolio worth approximately $200,000<\/strong>.<\/p>\n\n\n\n

\"\"\/<\/p>\n\n\n\n

We take three years of historical stock price data, which gives us more than 700 historical scenarios.<\/p>\n\n\n\n

\"\"\/<\/p>\n\n\n\n

Accordingly, we can calculate the portfolio\u2019s daily returns, which produces a frequency distribution of returns.<\/p>\n\n\n\n

\"\"\/<\/p>\n\n\n\n

If we then sort these scenarios, we can identify the threshold corresponding to our confidence level of interest.<\/p>\n\n\n\n

\"\"\/<\/p>\n\n\n\n

In the upper right part of the table, the 1-day risk is shown. The worst 1% of cases intersect at $6,279<\/strong>, while the average loss in those worst cases is $8,402<\/strong>.<\/p>\n\n\n\n

In the lower right part, the 1-day risk is transformed into a 10-day risk. As time increases, risk increases as well, using the following formula:<\/p>\n\n\n\n

N-day VaR = 1-day VaR \u00d7 \u221aN<\/strong><\/p>\n\n\n\n

It is interesting to ask:
$26,000 \/ $200,000 = 13% \u2014 how risky is that parameter?<\/strong>
It depends on the type of portfolio:<\/p>\n\n\n\n

Copilot:<\/p>\n\n\n\n

Portfolio<\/th>Typical 10-day VaR Range<\/th>Is 13% High?<\/th><\/tr><\/thead>
Equity index portfolio<\/td>3\u20138%<\/td>High<\/td><\/tr>
Single-name equities \/ concentrated book<\/td>8\u201320%<\/td>Normal<\/td><\/tr>
Options \/ volatility trading<\/td>15\u201340%<\/td>Low\u2013moderate<\/td><\/tr>
Crypto<\/td>20\u201360%<\/td>Low<\/td><\/tr>
Fixed income<\/td>1\u20134%<\/td>Very high<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\n

P.S.<\/strong>
VaR \u2013 Historical Simulation \u2013 Excel<\/a><\/p>\n\n\n\n

\u10d0\u10d3\u10d0\u10de\u10e2\u10d8\u10e0\u10d4\u10d1\u10e3\u10da\u10d8\u10d0 \u10ec\u10e7\u10d0\u10e0\u10dd\u10d3\u10d0\u10dc:
Options, Futures & Other Derivatives<\/em>, John C. Hull<\/p>\n\n\n\n

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\u10db\u10d0\u10e8\u10d8\u10dc \u10e0\u10dd\u10ea\u10d0 \u10d1\u10d4\u10e0\u10eb\u10dc\u10e3\u10da\u10d8 \u10e1\u10d8\u10db\u10d1\u10dd\u10da\u10dd\u10d4\u10d1\u10d8 \u10de\u10dd\u10e0\u10d7\u10e4\u10d4\u10da\u10d8\u10e1 \u10e0\u10d8\u10e1\u10d9\u10e1 \u10db\u10e0\u10d0\u10d5\u10d0\u10da\u10d8 \u10d9\u10e3\u10d7\u10ee\u10d8\u10d3\u10d0\u10dc \u10ee\u10d4\u10d3\u10d0\u10d5\u10d4\u10dc \u10d3\u10d0 n \u10e0\u10d0\u10dd\u10d3\u10d4\u10dc\u10dd\u10d1\u10d8\u10d7 \u10db\u10d0\u10e9\u10d5\u10d4\u10dc\u10d4\u10d1\u10da\u10d4\u10d1\u10e1 \u10d0\u10d2\u10d4\u10dc\u10d4\u10e0\u10d8\u10e0\u10d4\u10d1\u10d4\u10dc, VaR (Value at Risk) \u10db\u10d0\u10e9\u10d5\u10d4\u10dc\u10d4\u10d1\u10d4\u10da\u10d8 \u10d0\u10e0\u10d8\u10e1 \u10db\u10ea\u10d3\u10d4\u10da\u10dd\u10d1\u10d0 \u10d8\u10db\u10d8\u10e1\u10d0 \u10e0\u10dd\u10db \u10de\u10dd\u10e0\u10d7\u10e4\u10d4\u10da\u10d8\u10e1 \u10e0\u10d8\u10e1\u10d9\u10d8 \u10d4\u10e0\u10d7 \u10de\u10d0\u10e0\u10d0\u10db\u10d4\u10e2\u10e0\u10e8\u10d8 \u10d2\u10d0\u10db\u10dd\u10d8\u10ee\u10d0\u10e2\u10dd\u10e1. \u10d8\u10e1 \u10de\u10d0\u10e1\u10ee\u10e3\u10e1 \u10ea\u10d4\u10db\u10e1 \u10d3\u10d0\u10d0\u10ee\u10da\u10dd\u10d4\u10d1\u10d8\u10d7 [\u2026]<\/p>","protected":false},"author":12998525,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_eon_insights_quality":"","_eon_insights_decision":"","_eon_insights_destination":"","_eon_insights_merge_group":"","_eon_insights_required_changes":"","_eon_insights_start_order":0,"_eon_featured_insight":0,"_eon_insights_map_version":"","_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[31110612,784237235,106538530],"tags":[],"eon_topic":[],"eon_learning_path":[],"eon_collection":[],"eon_level":[],"eon_content_type":[],"eon_source":[],"eon_idea":[784445705],"eon_framework":[],"class_list":["post-8465","post","type-post","status-publish","format-standard","hentry","category-excel-models","category-options-futures-other-derivatives-john-c-hull-ka","category-derivatives","eon_idea-derivatives"],"yoast_head":"\nValue at Risk - 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